Algebraic Cycles and Topology of Real Algebraic Varieties PDF Download
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Author: Joost A. van Hamel
Publisher:
ISBN:
Category : Algebraic cycles
Languages : en
Pages : 156
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Book Description
Author: Joost A. van Hamel
Publisher:
ISBN:
Category : Algebraic cycles
Languages : en
Pages : 156
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Book Description
Author: Burt Totaro
Publisher: Cambridge University Press
ISBN: 1107015774
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Author: Frédéric Mangolte
Publisher: Springer Nature
ISBN: 3030431045
Category : Mathematics
Languages : en
Pages : 453
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Book Description
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.
Author: Shiing-Shen Chern
Publisher: World Scientific
ISBN: 9812776923
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."
Author: Spencer Bloch
Publisher: Cambridge University Press
ISBN: 1139487825
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch–Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycles on an algebraic variety can be infinite-dimensional, and explains how Hodge theory and algebraic K-theory give new insights into this and other phenomena.
Author: Frederic Mangolte
Publisher:
ISBN: 9782856298572
Category : Functions of real variables
Languages : fr
Pages : 180
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Book Description
Nous présentons dans ce volume de Panoramas et Synthèses un état des lieux de la recherche en géométrie algébrique réelle. Une introduction et cinq articles de synthèses composent ce volume. Les thématiques abordées sont : surfaces rationnelles réelles, géométrie o-minimales, arcs analytiques et singularités analytiques réelles, algorithmes en géométrie algébrique réelle, polynômes positifs et sommes de carrés. Ce volume s'adresse à un large public : les étudiants, les jeunes chercheurs dans le domaine et également les chercheurs confirmés non-spécialistes en géométrie algébrique réelle. [4ème de couv.].
Author: Saugata Basu
Publisher: Springer Science & Business Media
ISBN: 3662053551
Category : Mathematics
Languages : en
Pages : 602
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Book Description
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Author: Claire Voisin
Publisher: Princeton University Press
ISBN: 0691160511
Category : Mathematics
Languages : en
Pages : 171
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Book Description
In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.
Author: Piotr Pragacz
Publisher: Springer Science & Business Media
ISBN: 3764373423
Category : Mathematics
Languages : en
Pages : 321
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Book Description
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
Author: Bjorn Poonen
Publisher: American Mathematical Soc.
ISBN: 1470437732
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
