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Genre/Form: | Electronic books |
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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 title delves into arguments originating in Nori's work that have been further developed by others.
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Publisher Synopsis
"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 advanced] reader will find a rich collection of ideas as well as detailed machinery with which to attack difficult problems in the field. Any complex geometer interested in the interplay between algebraic cycles, Hodge theory and algebraic topology should have this book on his or her shelf."--C. A. M. Peters, Mathematical Reviews Clippings Read more...
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