On The Tangent Space To The Space Of Algebraic Cycles On A Smooth Algebraic Variety Am 157
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On The Tangent Space To The Space Of Algebraic Cycles On A Smooth Algebraic Variety Am 157
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Author : Mark Green
language : en
Publisher: Princeton University Press
Release Date : 2005-01-09
On The Tangent Space To The Space Of Algebraic Cycles On A Smooth Algebraic Variety Am 157 written by Mark Green and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-09 with Mathematics categories.
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Algebraic Cycles Sheaves Shtukas And Moduli
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Author : Piotr Pragacz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-12
Algebraic Cycles Sheaves Shtukas And Moduli written by Piotr Pragacz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-12 with Mathematics categories.
Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Tangents And Secants Of Algebraic Varieties
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Author : F. L. Zak
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Tangents And Secants Of Algebraic Varieties written by F. L. Zak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
"The book is devoted to geometry of algebraic varieties in projective spaces. Among the objects considered in some detail are tangent and secant varieties, Gauss maps, dual varieties, hyperplane sections, projections, and varieties of small codimension. Emphasis is made on the study of interplay between irregular behavior of (higher) secant varieties and irregular tangencies to the original variety. Classification of varieties with unusual tangential properties yields interesting examples many of which arise as orbits of representations of algebraic groups."--ABSTRACT.
Lectures On Algebraic Cycles
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Author : Spencer Bloch
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-22
Lectures On Algebraic Cycles written by Spencer Bloch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-22 with Mathematics categories.
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.
Algebraic Cycles And Motives Volume 1
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Author : Jan Nagel
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-03
Algebraic Cycles And Motives Volume 1 written by Jan Nagel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-03 with Mathematics categories.
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
The Arithmetic And Geometry Of Algebraic Cycles
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Author : B. Brent Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-29
The Arithmetic And Geometry Of Algebraic Cycles written by B. Brent Gordon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.
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.
Transcendental Aspects Of Algebraic Cycles
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Author : S. Müller-Stach
language : en
Publisher: Cambridge University Press
Release Date : 2004-04-20
Transcendental Aspects Of Algebraic Cycles written by S. Müller-Stach and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-20 with Mathematics categories.
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Topics In Transcendental Algebraic Geometry Am 106 Volume 106
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Author : Phillip A. Griffiths
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Topics In Transcendental Algebraic Geometry Am 106 Volume 106 written by Phillip A. Griffiths and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
A classic treatment of transcendental algebraic geometry from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-12-16
Algebraic Cycles And Hodge Theory written by Mark L. Green and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with Mathematics categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.