The Geometry Of Some Special Arithmetic Quotients

Author : Bruce Hunt
Publisher : Springer
Page : 347 pages
File Size : 41,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540699972

Get Book

The Geometry of some special Arithmetic Quotients by Bruce Hunt Pdf

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 570 pages
File Size : 45,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821844762

Get Book

Arithmetic Geometry by Clay Mathematics Institute. Summer School Pdf

Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 47,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

Get Book

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Radu Laza,Matthias Schütt,Noriko Yui Pdf

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Author : V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 55,8 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781470418717

Get Book

Topology, Geometry, Integrable Systems, and Mathematical Physics by V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever Pdf

Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 876 pages
File Size : 53,6 Mb
Release : 2007
Category : Teichm uller spaces
ISBN : 3037191031

Get Book

Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.

Author : Paolo Cascini,James McKernan,Jorge Vitório Pereira
Publisher : Springer
Page : 216 pages
File Size : 48,8 Mb
Release : 2016-03-30
Category : Mathematics
ISBN : 9783319244600

Get Book

Foliation Theory in Algebraic Geometry by Paolo Cascini,James McKernan,Jorge Vitório Pereira Pdf

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

Author : Claude P. Bruter
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 41,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662049099

Get Book

Mathematics and Art by Claude P. Bruter Pdf

Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.

Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 49,6 Mb
Release : 1999-10-19
Category : Mathematics
ISBN : 3540665463

Get Book

Arithmetic Theory of Elliptic Curves by J. Coates,R. Greenberg,K.A. Ribet,K. Rubin Pdf

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Author : Károly Jr. Böröczky,János Kollár,Szamuely Tamas
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 46,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662051238

Get Book

Higher Dimensional Varieties and Rational Points by Károly Jr. Böröczky,János Kollár,Szamuely Tamas Pdf

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Author : A. Jon Berrick,Man Chun Leung,Singapore International Symposium in Topology and Geometry,Xingwang Xu
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 55,9 Mb
Release : 2002
Category : Geometry
ISBN : 9780821828205

Get Book

Topology and Geometry: Commemorating SISTAG by A. Jon Berrick,Man Chun Leung,Singapore International Symposium in Topology and Geometry,Xingwang Xu Pdf

This volume presents 19 refereed articles written by participants in the Singapore International Symposium in Topology and Geometry (SISTAG), held July 2-6, 2001, at the National University of Singapore. Rather than being a simple snapshot of the meeting in the form of a proceedings, it serves as a commemorative volume consisting of papers selected to show the diversity and depth of the mathematics presented at SISTAG. The book contains articles on low-dimensional topology, algebraic, differential and symplectic geometry, and algebraic topology. While papers reflect the focus of the conference, many documents written after SISTAG and included in this volume represent the most up-to-date thinking in the fields of topology and geometry. While representation from Pacific Rim countries is strong, the list of contributors is international in scope and includes many recognized experts. This volume is of interest to graduate students and mathematicians working in the fields of algebraic, differential and symplectic geometry, algebraic, geometric and low-dimensional topology, and mathematical physics.

Author : Ulrich Görtz,Torsten Wedhorn
Publisher : Springer Science & Business Media
Page : 615 pages
File Size : 41,8 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9783834897220

Get Book

Algebraic Geometry by Ulrich Görtz,Torsten Wedhorn Pdf

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Author : Bernhard Schmidt
Publisher : Springer
Page : 108 pages
File Size : 48,6 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540457978

Get Book

Characters and Cyclotomic Fields in Finite Geometry by Bernhard Schmidt Pdf

This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 46,6 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

Get Book

CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814477048

Get Book

Singularities in Geometry and Topology by Anonim Pdf

Author : Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 50,8 Mb
Release : 1998-04-16
Category : Mathematics
ISBN : 3540642072

Get Book

Integral Geometry, Radon Transforms and Complex Analysis by Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov Pdf

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.