Chow Rings, Decomposition of the Diagonal, and the Topology of Families, Pape...

Description: Chow Rings, Decomposition of the Diagonal, and the Topology of Families, Paperback by Voisin, Claire, ISBN 0691160511, ISBN-13 9780691160511, Like New Used, Free P&P in the UK

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. Th 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-Khler manifolds. In particular, th delves into arguments originating in Noris work that have been further developed by others.

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End Time: 2024-12-19T21:41:35.000Z

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