Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 42,8 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

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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 : Radu Laza,Matthias Schutt,Noriko Yui
Publisher : Unknown
Page : 630 pages
File Size : 47,8 Mb
Release : 2013-07-31
Category : Electronic
ISBN : 1461464048

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

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 46,7 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042

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Lectures on K3 Surfaces by Daniel Huybrechts Pdf

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Author : Christian Meyer
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 49,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871811

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Modular Calabi-Yau Threefolds by Christian Meyer Pdf

The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer
Page : 547 pages
File Size : 46,6 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781493928309

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Calabi-Yau Varieties: Arithmetic, Geometry and Physics by Radu Laza,Matthias Schütt,Noriko Yui Pdf

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Author : Noriko Yui,James Dominic Lewis
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 48,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871439

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Calabi-Yau Varieties and Mirror Symmetry by Noriko Yui,James Dominic Lewis Pdf

The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.

Author : Carel Faber,Gavril Farkas,Gerard van der Geer
Publisher : Birkhäuser
Page : 399 pages
File Size : 51,7 Mb
Release : 2016-04-22
Category : Mathematics
ISBN : 9783319299594

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K3 Surfaces and Their Moduli by Carel Faber,Gavril Farkas,Gerard van der Geer Pdf

This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Author : Marie José Bertin,Alina Bucur,Brooke Feigon,Leila Schneps
Publisher : Springer
Page : 205 pages
File Size : 44,7 Mb
Release : 2015-09-22
Category : Mathematics
ISBN : 9783319179872

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Women in Numbers Europe by Marie José Bertin,Alina Bucur,Brooke Feigon,Leila Schneps Pdf

Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,6 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9781461464822

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Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Author : Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher : Cambridge University Press
Page : 451 pages
File Size : 43,7 Mb
Release : 2015-01-15
Category : Mathematics
ISBN : 9781107647558

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Recent Advances in Algebraic Geometry by Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa Pdf

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Author : B. Brent Gordon,James D. Lewis,Stefan Müller-Stach,Shuji Saito,Noriko Yui
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 55,8 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 0792361946

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The Arithmetic and Geometry of Algebraic Cycles by B. Brent Gordon,James D. Lewis,Stefan Müller-Stach,Shuji Saito,Noriko Yui Pdf

The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.

Author : Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini
Publisher : Springer Nature
Page : 421 pages
File Size : 53,9 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783031119385

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The Art of Doing Algebraic Geometry by Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini Pdf

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

Author : Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 45,8 Mb
Release : 2006-09-29
Category : Mathematics
ISBN : 9783540354802

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Global Aspects of Complex Geometry by Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell Pdf

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Author : Matthias Schütt,Tetsuji Shioda
Publisher : Springer Nature
Page : 431 pages
File Size : 43,9 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 : Jennifer S. Balakrishnan,Amanda Folsom,Matilde Lalín,Michelle Manes
Publisher : Springer
Page : 195 pages
File Size : 52,8 Mb
Release : 2019-08-01
Category : Mathematics
ISBN : 9783030194789

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Research Directions in Number Theory by Jennifer S. Balakrishnan,Amanda Folsom,Matilde Lalín,Michelle Manes Pdf

These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well as other original research contributions involving participants of the WIN workshops. The workshop and this volume are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields.