| Description |
1 online resource (172 pages) |
| Series |
Annals of Mathematics Studies |
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Annals of mathematics studies.
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| 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 |
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""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-KÃ?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"" |
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""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"" |
| 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 dependi |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Algebraic varieties.
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Decomposition (Mathematics)
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Homology theory.
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Algebraic varieties
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Decomposition (Mathematics)
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Homology theory
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Mathematics.
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Physical Sciences & Mathematics.
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Geometry.
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| Form |
Electronic book
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| ISBN |
9780691160504 |
|
0691160503 |
|
1400850533 |
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9781400850532 |
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