Claire Voisin

(Author)

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (Am-187)Paperback, 23 February 2014

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (Am-187)
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Part of Series
Annals of Mathematics Studies
Part of Series
Annals of Mathematics Studies (Paperback)
Print Length
176 pages
Language
English
Publisher
Princeton University Press
Date Published
23 Feb 2014
ISBN-10
0691160511
ISBN-13
9780691160511

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

Product Details

Author:
Claire Voisin
Book Format:
Paperback
Country of Origin:
US
Date Published:
23 February 2014
Dimensions:
23.11 x 15.49 x 1.52 cm
ISBN-10:
0691160511
ISBN-13:
9780691160511
Language:
English
Location:
Princeton
Pages:
176
Weight:
294.83 gm

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