Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187). (eBook, 2014) [WorldCat.org]
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Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187).
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Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187).

Author: Claire Voisin
Publisher: Princeton University Press, 2014.
Series: Annals of mathematics studies.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Voisin, Claire.
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187).
: Princeton University Press, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Claire Voisin
ISBN: 9780691160504 0691160503 1400850533 9781400850532
OCLC Number: 922907319
Language Note: English.
Description: 1 online resource (172 pages)
Contents: ""Cover""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""1 Introduction""; ""1.1 Decomposition of the diagonal and spread""; ""1.2 The generalized Bloch conjecture""; ""1.3 Decomposition of the small diagonal and application to the topology of families""; ""1.4 Integral coefficients and birational invariants""; ""1.5 Organization of the text""; ""2 Review of Hodge theory and algebraic cycles""; ""2.1 Chow groups""; ""2.2 Hodge structures""; ""3 Decomposition of the diagonal""; ""3.1 A general principle""; ""3.2 Varieties with small Chow groups"" ""4 Chow groups of large coniveau complete intersections""""4.1 Hodge coniveau of complete intersections""; ""4.2 Coniveau 2 complete intersections""; ""4.3 Equivalence of generalized Bloch and Hodge conjectures for general complete intersections""; ""4.4 Further applications to the Bloch conjecture on 0-cycles on surfaces""; ""5 On the Chow ring of K3 surfaces and hyper-K�hler manifolds""; ""5.1 Tautological ring of a K3 surface""; ""5.2 A decomposition of the small diagonal""; ""5.3 Deligne's decomposition theorem for families of K3 surfaces""; ""6 Integral coefficients"" ""6.1 Integral Hodge classes and birational invariants""""6.2 Rationally connected varieties and the rationality problem""; ""6.3 Integral decomposition of the diagonal and the structure of the Abel�Jacobi map""; ""Bibliography""; ""Index""
Series Title: Annals of mathematics studies.

Abstract:

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. This  Read more...

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"This dense, fascinating book by Voisin is a report of some of the exciting discoveries she has made in the quest of the secrets of algebraic cycles."--Alberto Collino, Zentralblatt MATH "[An Read more...

 
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