16 6 Configurations And Geometry Of Kummer Surfaces In Mathbb P 3

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 44,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825747

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$(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ by Maria del Rosario Gonzalez-Dorrego Pdf

The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Society(RI)
Page : 114 pages
File Size : 43,6 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400898

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16,6 Configurations and Geometry of Kummer Surfaces in by Maria del Rosario Gonzalez-Dorrego Pdf

This monograph studies the geometry of a Summer surface in P ]3 and of its minimal desingularization, which is a K3 surface (here k is an algebraically closed field of characteristic different from 2). This Kummer surface is a quartic surface with sixteen nodes as its only singularities. These nodes give rise to a configuration of sixteen points and sixteen planes in P ]3 such that each plane contains exactly six points and each point belongs to exactly six planes (this is called a (16, 6) configuration). A Kummer surface is uniquely determined by its set of nodes. Gonzalez_Dorrego classifies (16, 6) configurations and studies their manifold symmetries and the underlying questions about finite subgroups of PGL [4 ( k ). She uses this information to give a complete classification of Kummer surfaces with explicit equations and explicit descriptions of their singularities. In addition, the beautiful connections to the theory of K3 surfaces and abelian varieties are studied.

Author : Mauro Beltrametti,Michael Schneider,Andrew John Sommese
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 54,8 Mb
Release : 1995
Category : Adjunction theory
ISBN : 9780821802342

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Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ by Mauro Beltrametti,Michael Schneider,Andrew John Sommese Pdf

This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.

Author : Ronald William Henry Turnbull Hudson
Publisher : Unknown
Page : 54 pages
File Size : 54,6 Mb
Release : 1905
Category : Functions, Theta
ISBN : PSU:000003391174

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Kummer's Quartic Surface by Ronald William Henry Turnbull Hudson Pdf

Author : Matthias Schütt,Tetsuji Shioda
Publisher : Springer Nature
Page : 431 pages
File Size : 48,7 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789813293014

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Mordell–Weil Lattices by Matthias Schütt,Tetsuji Shioda Pdf

This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.

Author : J. Elias,J. M. Giral,Rosa M. Miró-Roig,Santiago Zarzuela
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 52,7 Mb
Release : 2010-03-17
Category : Mathematics
ISBN : 9783034603294

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Six Lectures on Commutative Algebra by J. Elias,J. M. Giral,Rosa M. Miró-Roig,Santiago Zarzuela Pdf

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH

Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 53,9 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780521734714

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Moduli Spaces and Vector Bundles by Steve Bradlow Pdf

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 40,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719208

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The Arithmetic of Elliptic Curves by Joseph H. Silverman Pdf

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Author : Pietro Giuseppe Frè
Publisher : Springer
Page : 556 pages
File Size : 53,8 Mb
Release : 2018-02-24
Category : Science
ISBN : 9783319744919

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Advances in Geometry and Lie Algebras from Supergravity by Pietro Giuseppe Frè Pdf

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.

Author : Bruce Hunt
Publisher : Springer Nature
Page : 622 pages
File Size : 51,8 Mb
Release : 2021-09-04
Category : Mathematics
ISBN : 9783030698041

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Locally Mixed Symmetric Spaces by Bruce Hunt Pdf

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Author : Nicholas M. Katz
Publisher : Princeton University Press
Page : 236 pages
File Size : 46,6 Mb
Release : 1996
Category : Mathematics
ISBN : 0691011184

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Rigid Local Systems by Nicholas M. Katz Pdf

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.

Author : Gary T. Horowitz
Publisher : Cambridge University Press
Page : 437 pages
File Size : 41,9 Mb
Release : 2012-04-19
Category : Science
ISBN : 9781107013452

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Black Holes in Higher Dimensions by Gary T. Horowitz Pdf

The first book devoted to black holes in more than four dimensions, for graduate students and researchers.

Author : Valery A. Gritsenko,Vyacheslav P. Spiridonov
Publisher : Springer Nature
Page : 422 pages
File Size : 50,7 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9783030424008

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Partition Functions and Automorphic Forms by Valery A. Gritsenko,Vyacheslav P. Spiridonov Pdf

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Author : James H. Davenport,Manuel Kauers,George Labahn,Josef Urban
Publisher : Springer
Page : 508 pages
File Size : 42,9 Mb
Release : 2018-07-17
Category : Computers
ISBN : 9783319964188

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Mathematical Software – ICMS 2018 by James H. Davenport,Manuel Kauers,George Labahn,Josef Urban Pdf

This book constitutes the proceedings of the 6th International Conference on Mathematical Software, ICMS 2018, held in South Bend, IN, USA, in July 2018.The 59 papers included in this volume were carefully reviewed and selected from numerous submissions. The program of the 2018 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a subeld of mathematical software research, development and use.

Author : Gianluca Calcagni
Publisher : Springer
Page : 843 pages
File Size : 48,6 Mb
Release : 2017-01-06
Category : Science
ISBN : 9783319411279

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Classical and Quantum Cosmology by Gianluca Calcagni Pdf

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.