Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

By:

Claire Voisin

Format:

Paperback / softback

Series:

Annals of Mathematics Studies

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Description

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-Kahler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

Author Biography:

Claire Voisin has been a senior researcher at France's National Center for Scientific Research since 1986.

Release date NZ

February 23rd, 2014

Author

Claire Voisin

Audiences

Professional & Vocational
Tertiary Education (US: College)

Pages

176

Series

Annals of Mathematics Studies

Dimensions

152x229x15

ISBN-13

9780691160511

Product ID

21743790

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