Real Enriques Surfaces
Real Enriques Surfaces

Author: Alexander Degtyarev

Publisher: Springer

Published: 2007-05-06

Total Pages: 275

ISBN-13: 3540399488

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This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces.

Topology, Ergodic Theory, Real Algebraic Geometry
Topology, Ergodic Theory, Real Algebraic Geometry

Author: Vladimir G. Turaev

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 300

ISBN-13: 9780821827406

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This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.

Real Algebraic Varieties
Real Algebraic Varieties

Author: Frédéric Mangolte

Publisher: Springer Nature

Published: 2020-09-21

Total Pages: 453

ISBN-13: 3030431045

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This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.

Contemporary Trends In Algebraic Geometry And Algebraic Topology
Contemporary Trends In Algebraic Geometry And Algebraic Topology

Author: Shiing-shen Chern

Publisher: World Scientific

Published: 2002-08-02

Total Pages: 276

ISBN-13: 9814488518

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The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc.This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fiber spaces, and others.

Conformal Geometry of Discrete Groups and Manifolds
Conformal Geometry of Discrete Groups and Manifolds

Author: Boris N. Apanasov

Publisher: Walter de Gruyter

Published: 2011-06-24

Total Pages: 541

ISBN-13: 3110808056

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Algebraic Geometry and its Applications
Algebraic Geometry and its Applications

Author: Alexander Tikhomirov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 264

ISBN-13: 3322993426

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This volume contains 18 papers at the Algebraic Geometry Conference, Yaroslavl', August 10-14, 1992. These conferences in algebraic geometry have a great tradition in Russia and are helt since 1979 in Yaroslavl' every second year. The present conference, the eighth one, was the first in which several foreign mathematicians participated. From the Russian side, there was a large group of specialists in algebraic geometry and related fields (invariant theory, topology of manifolds, theory of categories, mathematical physics etc.). Lectures on modern directions in algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to Donaldson's theory, geometry of Hilbert schemes of points, twistor spaces and applications to string theory, and more traditional areas, such as birational geometry of manifolds, adjunction theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties, and others are contained in this volume.

Algebraic Geometry
Algebraic Geometry

Author: Mauro C. Beltrametti

Publisher: Walter de Gruyter

Published: 2008-08-22

Total Pages: 364

ISBN-13: 311019807X

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The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type. A part of the articles grew out a Conference in memory of Paolo Francia (1951-2000) held in Genova in September 2001 with about 70 participants.