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The Resource Chow rings, decomposition of the diagonal, and the topology of families, Claire Voisin

Chow rings, decomposition of the diagonal, and the topology of families, Claire Voisin

Label
Chow rings, decomposition of the diagonal, and the topology of families
Title
Chow rings, decomposition of the diagonal, and the topology of families
Statement of responsibility
Claire Voisin
Creator
Author
Subject
Language
eng
Summary
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. --Provided by publisher
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1962-
http://library.link/vocab/creatorName
Voisin, Claire
Dewey number
516.3/5
Index
index present
LC call number
QA564
LC item number
.V648 2014
Literary form
non fiction
Nature of contents
bibliography
Series statement
Annals of Mathematics studies
Series volume
number 187
http://library.link/vocab/subjectName
  • Algebraic varieties
  • Decomposition (Mathematics)
  • Homology theory
Label
Chow rings, decomposition of the diagonal, and the topology of families, Claire Voisin
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 155-162) and index
Carrier category
volume
Carrier MARC source
rdacarrier.
Content category
text
Content type MARC source
rdacontent.
Contents
Introduction -- Review of Hodge theory and algebraic cycles -- Decomposition of the diagonal -- Chow groups of large coniveau complete intersections -- On the Chow ring of K3 surfaces and hyper-Kahler manifolds -- Integral coefficients
Control code
852745692
Dimensions
24 cm
Extent
viii, 162 pages
Isbn
9780691160504
Isbn Type
(cloth : alk. paper)
Lccn
2013016992
Media category
unmediated
Media MARC source
rdamedia.
System control number
(OCoLC)852745692
Label
Chow rings, decomposition of the diagonal, and the topology of families, Claire Voisin
Publication
Bibliography note
Includes bibliographical references (pages 155-162) and index
Carrier category
volume
Carrier MARC source
rdacarrier.
Content category
text
Content type MARC source
rdacontent.
Contents
Introduction -- Review of Hodge theory and algebraic cycles -- Decomposition of the diagonal -- Chow groups of large coniveau complete intersections -- On the Chow ring of K3 surfaces and hyper-Kahler manifolds -- Integral coefficients
Control code
852745692
Dimensions
24 cm
Extent
viii, 162 pages
Isbn
9780691160504
Isbn Type
(cloth : alk. paper)
Lccn
2013016992
Media category
unmediated
Media MARC source
rdamedia.
System control number
(OCoLC)852745692

Library Locations

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