Booktopia has been placed into Voluntary Administration. Orders have been temporarily suspended, whilst the process for the recapitalisation of Booktopia and/or sale of its business is completed, following which services may be re-established. All enquiries from creditors, including customers with outstanding gift cards and orders and placed prior to 3 July 2024, please visit https://www.mcgrathnicol.com/creditors/booktopia-group/

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

By: Claire Voisin

Write A Review

eBook | 23 February 2014 | Edition Number 1

At a Glance

ePUB
176 Pages

Edition Type
Course Book

eBook

RRP $151.80

$121.99

20%OFF

or 4 interest-free payments of $30.50 with

Instant Digital Delivery to your Booktopia Reader App

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.

Industry Reviews

"[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