Integrable Systems in the realm of Algebraic Geometry
Integrable Systems in the realm of Algebraic Geometry

Author: Pol Vanhaecke

Publisher: Springer

Published: 2013-11-11

Total Pages: 226

ISBN-13: 3662215357

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Integrable systems are related to algebraic geometry in many different ways. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. For a rigorous account of these matters, integrable systems are defined on affine algebraic varieties rather than on smooth manifolds. The exposition is self-contained and is accessible at the graduate level; in particular, prior knowledge of integrable systems is not assumed.

Algebraic and Complex Geometry
Algebraic and Complex Geometry

Author: Anne Frühbis-Krüger

Publisher: Springer

Published: 2014-10-01

Total Pages: 324

ISBN-13: 331905404X

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Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the first author. It also includes a full list of speakers with all titles and abstracts.

Selected Topics in Algebraic Geometry
Selected Topics in Algebraic Geometry

Author: National Research Council (U.S.). Committee on Rational Transformations

Publisher: American Mathematical Soc.

Published: 1970

Total Pages: 518

ISBN-13: 9780828401890

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This book resulted from two reports (published in 1928 and 1932) of the Committee on Rational Transformations, established by the National Research Council. The purpose of the reports was to give a comprehensive survey of the literature on the subject. Each chapter is regarded as a separate unit that can be read independently.

Integrable Systems and Algebraic Geometry
Integrable Systems and Algebraic Geometry

Author: Ron Donagi

Publisher: Cambridge University Press

Published: 2020-03-02

Total Pages: 537

ISBN-13: 110871577X

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A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Algebraic Geometry
Algebraic Geometry

Author: Igor V. Dolgachev

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 256

ISBN-13: 0821842013

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This volume contains the proceedings of the Korea-Japan Conference on Algebraic Geometry in honor of Igor Dolgachev on his sixtieth birthday. The articles in this volume explore a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered by this volume are algebraic curve theory, algebraic surface theory, moduli space, automorphic forms, Mordell-Weil lattices, and automorphisms of hyperkahler manifolds. This book is an excellent and rich reference source for researchers.

Integrable Systems and Algebraic Geometry: Volume 2
Integrable Systems and Algebraic Geometry: Volume 2

Author: Ron Donagi

Publisher: Cambridge University Press

Published: 2020-04-02

Total Pages: 537

ISBN-13: 1108805337

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Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.

Algebraic Integrability, Painlevé Geometry and Lie Algebras
Algebraic Integrability, Painlevé Geometry and Lie Algebras

Author: Mark Adler

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 487

ISBN-13: 366205650X

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This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.

The Art of Doing Algebraic Geometry
The Art of Doing Algebraic Geometry

Author: Thomas Dedieu

Publisher: Springer Nature

Published: 2023-04-14

Total Pages: 421

ISBN-13: 303111938X

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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.