Geometric And Combinatorial Aspects Of Commutative Algebra

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Geometric And Combinatorial Aspects Of Commutative Algebra

Jurgen Herzog,Gaetana Restuccia
Geometric And Combinatorial Aspects Of Commutative Algebra Book PDF

Author : Jurgen Herzog,Gaetana Restuccia
Publisher : CRC Press
Page : 424 pages
File Size : 42,6 Mb
Release : 2001-03-06
Category : Mathematics
ISBN : 0203908015

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Geometric And Combinatorial Aspects Of Commutative Algebra by Jurgen Herzog,Gaetana Restuccia Pdf

This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable idea

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Combinatorial Aspects of Commutative Algebra and Algebraic Geometry Book PDF

Author : Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 42,6 Mb
Release : 2011-05-16
Category : Mathematics
ISBN : 9783642194924

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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry by Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen Pdf

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Combinatorial Aspects of Commutative Algebra and Algebraic Geometry Book PDF

Author : Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Publisher : Springer
Page : 174 pages
File Size : 44,5 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 3642194915

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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry by Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen Pdf

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.

Combinatorial Aspects of Commutative Algebra

Viviana Ene,Ezra Miller
Combinatorial Aspects of Commutative Algebra Book PDF

Author : Viviana Ene,Ezra Miller
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 46,8 Mb
Release : 2009-11-25
Category : Mathematics
ISBN : 9780821847589

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Combinatorial Aspects of Commutative Algebra by Viviana Ene,Ezra Miller Pdf

This volume contains the proceedings of the Exploratory Workshop on Combinatorial Commutative Algebra and Computer Algebra, which took place in Mangalia, Romania on May 29-31, 2008. It includes research papers and surveys reflecting some of the current trends in the development of combinatorial commutative algebra and related fields. This volume focuses on the presentation of the newest research results in minimal resolutions of polynomial ideals (combinatorial techniques and applications), Stanley-Reisner theory and Alexander duality, and applications of commutative algebra and of combinatorial and computational techniques in algebraic geometry and topology. Both the algebraic and combinatorial perspectives are well represented and some open problems in the above directions have been included.

Commutative Algebra

Alberto Corso
Commutative Algebra Book PDF

Author : Alberto Corso
Publisher : CRC Press
Page : 128 pages
File Size : 41,7 Mb
Release : 2017-08-09
Category : Electronic
ISBN : 1138402125

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Commutative Algebra by Alberto Corso Pdf

Packed with contributions from international experts, Commutative Algebra: Geometric, Homological, Combinatorial, and Computational Aspects features new research results that borrow methods from neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation, and topology. This book consists of articles presented during two conferences held in Spain and Portugal in June, 2003. It encompasses a variety of topics, including blowup algebras, Castelnuovo-Mumford regularity, integral closure and normality, Koszul homology, liaison theory, multiplicities, polarization, and reductions of ideals. This comprehensive volume will stimulate further research in the field.

Combinatorial Commutative Algebra

Ezra Miller,Bernd Sturmfels
Combinatorial Commutative Algebra Book PDF

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 44,9 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Commutative Algebra

Aron Simis
Commutative Algebra Book PDF

Author : Aron Simis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 495 pages
File Size : 46,9 Mb
Release : 2023-08-07
Category : Mathematics
ISBN : 9783111078847

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Commutative Algebra by Aron Simis Pdf

The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth).

Commutative Algebra - Proceedings Of The Workshop

Giuseppe Valla,Ngo Viet Trung,Aron Simis
Commutative Algebra Proceedings Of The Workshop Book PDF

Author : Giuseppe Valla,Ngo Viet Trung,Aron Simis
Publisher : World Scientific
Page : 330 pages
File Size : 49,7 Mb
Release : 1994-08-19
Category : Electronic
ISBN : 9789814551793

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Commutative Algebra - Proceedings Of The Workshop by Giuseppe Valla,Ngo Viet Trung,Aron Simis Pdf

In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.

Ideals of Powers and Powers of Ideals

Enrico Carlini,Huy Tài Hà,Brian Harbourne,Adam Van Tuyl
Ideals of Powers and Powers of Ideals Book PDF

Author : Enrico Carlini,Huy Tài Hà,Brian Harbourne,Adam Van Tuyl
Publisher : Springer Nature
Page : 162 pages
File Size : 51,8 Mb
Release : 2020-05-21
Category : Mathematics
ISBN : 9783030452476

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Ideals of Powers and Powers of Ideals by Enrico Carlini,Huy Tài Hà,Brian Harbourne,Adam Van Tuyl Pdf

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.

Algebraic and Geometric Combinatorics

Christos A. Athanasiadis
Algebraic and Geometric Combinatorics Book PDF

Author : Christos A. Athanasiadis
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 55,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840801

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Algebraic and Geometric Combinatorics by Christos A. Athanasiadis Pdf

This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Combinatorial Structures in Algebra and Geometry

Dumitru I. Stamate,Tomasz Szemberg
Combinatorial Structures in Algebra and Geometry Book PDF

Author : Dumitru I. Stamate,Tomasz Szemberg
Publisher : Springer Nature
Page : 182 pages
File Size : 53,7 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030521110

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Combinatorial Structures in Algebra and Geometry by Dumitru I. Stamate,Tomasz Szemberg Pdf

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).

Progress in Commutative Algebra 1

Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Progress in Commutative Algebra 1 Book PDF

Author : Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 53,6 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110250404

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Progress in Commutative Algebra 1 by Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev Pdf

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.

Connections Between Algebra, Combinatorics, and Geometry

Susan M. Cooper,Sean Sather-Wagstaff
Connections Between Algebra Combinatorics and Geometry Book PDF

Author : Susan M. Cooper,Sean Sather-Wagstaff
Publisher : Springer
Page : 328 pages
File Size : 46,6 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9781493906260

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Connections Between Algebra, Combinatorics, and Geometry by Susan M. Cooper,Sean Sather-Wagstaff Pdf

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Lectures in Geometric Combinatorics

Rekha R. Thomas
Lectures in Geometric Combinatorics Book PDF

Author : Rekha R. Thomas
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 44,5 Mb
Release : 2006
Category : Mathematics
ISBN : 0821841408

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Lectures in Geometric Combinatorics by Rekha R. Thomas Pdf

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Commutative Algebra, Algebraic Geometry, and Computational Methods

David Eisenbud
Commutative Algebra Algebraic Geometry and Computational Methods Book PDF

Author : David Eisenbud
Publisher : Springer
Page : 346 pages
File Size : 42,6 Mb
Release : 1999-07
Category : Mathematics
ISBN : UOM:39015056636189

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Commutative Algebra, Algebraic Geometry, and Computational Methods by David Eisenbud Pdf

This volume contains papers presented at the International Conference on Commutative Algebra, Algebraic geometry, and Computational methods held in Hanoi in 1996, as well as papers written subsequently. It features both expository articles as well as research papers on a range of currently active areas in commutative algebra, algebraic geometry (particularly surveys on intersection theory) and combinatorics. In addition, a special feature is a section on the life and work of Wolfgang Vogel, who was an organiser of the conference.