Arc Schemes And Singularities

Author : David Bourqui,Johannes Nicaise,Julien Sebag
Publisher : World Scientific
Page : 312 pages
File Size : 49,6 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9781786347213

Get Book

Arc Schemes And Singularities by David Bourqui,Johannes Nicaise,Julien Sebag Pdf

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.

Author : José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade
Publisher : Springer Nature
Page : 622 pages
File Size : 52,5 Mb
Release : 2023-11-10
Category : Mathematics
ISBN : 9783031319259

Get Book

Handbook of Geometry and Topology of Singularities IV by José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade Pdf

This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Author : Javier Fernández de Bobadilla,Tamás László,András Stipsicz
Publisher : Springer Nature
Page : 332 pages
File Size : 44,6 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9783030619589

Get Book

Singularities and Their Interaction with Geometry and Low Dimensional Topology by Javier Fernández de Bobadilla,Tamás László,András Stipsicz Pdf

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Author : Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas
Publisher : American Mathematical Soc.
Page : 655 pages
File Size : 41,6 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435776

Get Book

Algebraic Geometry: Salt Lake City 2015 (Part 1) by Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas Pdf

This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Author : Maria Gorelik,Vladimir Hinich,Anna Melnikov
Publisher : Springer Nature
Page : 553 pages
File Size : 43,9 Mb
Release : 2019-10-18
Category : Mathematics
ISBN : 9783030235314

Get Book

Representations and Nilpotent Orbits of Lie Algebraic Systems by Maria Gorelik,Vladimir Hinich,Anna Melnikov Pdf

This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Author : Kurusch Ebrahimi-Fard
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 54,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853290

Get Book

Combinatorics and Physics by Kurusch Ebrahimi-Fard Pdf

This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Author : David Eisenbud,Joe Harris
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 52,7 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226392

Get Book

The Geometry of Schemes by David Eisenbud,Joe Harris Pdf

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Author : Geometry and Their Interactions International Conference on Midwest Algebra
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 50,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840948

Get Book

Algebra, Geometry and Their Interactions by Geometry and Their Interactions International Conference on Midwest Algebra Pdf

This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.

Author : Shihoko Ishii
Publisher : Springer
Page : 236 pages
File Size : 48,5 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9784431568377

Get Book

Introduction to Singularities by Shihoko Ishii Pdf

This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.

Author : Dan Abramovich
Publisher : American Mathematical Soc.
Page : 539 pages
File Size : 51,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847039

Get Book

Algebraic Geometry by Dan Abramovich Pdf

Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.

Author : Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag
Publisher : Springer
Page : 526 pages
File Size : 54,9 Mb
Release : 2018-09-15
Category : Mathematics
ISBN : 9781493978878

Get Book

Motivic Integration by Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag Pdf

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.

Author : David Mond,Juan J. Nuño-Ballesteros
Publisher : Springer Nature
Page : 567 pages
File Size : 44,5 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9783030344405

Get Book

Singularities of Mappings by David Mond,Juan J. Nuño-Ballesteros Pdf

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.

Author : Mircea Immanuel Mustaţǎ
Publisher : Unknown
Page : 130 pages
File Size : 45,5 Mb
Release : 2001
Category : Electronic
ISBN : UCAL:C3448304

Get Book

Singularities and Jet Schemes by Mircea Immanuel Mustaţǎ Pdf

Author : Cornelia Oichi Yuen
Publisher : Unknown
Page : 208 pages
File Size : 41,9 Mb
Release : 2006
Category : Electronic
ISBN : UOM:39015064784658

Get Book

Jet Schemes and Truncated Wedge Schemes by Cornelia Oichi Yuen Pdf

Author : Nero Budur,Tommaso de Fernex,Roi Docampo,Kevin Tucker
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 50,6 Mb
Release : 2018-07-26
Category : Festschriften
ISBN : 9781470434885

Get Book

Local and Global Methods in Algebraic Geometry by Nero Budur,Tommaso de Fernex,Roi Docampo,Kevin Tucker Pdf

This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.