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

Print publication date: 2014

Print ISBN-13: 9780691160504

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691160504.001.0001

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Introduction

Introduction

Chapter:
(p.1) Chapter One Introduction
Source:
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)
Author(s):

Claire Voisin

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691160504.003.0001

This chapter discusses some crucial notions to the interplay between cohomology and Chow groups, and also to the consequences, for the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general or very general fiber. It surveys the main ideas and results presented throughout this volume. First, the chapter discusses the decomposition of the diagonal and spread. It then explains the generalized Bloch conjecture, the converse to the generalized decomposition of the diagonal. Next, the chapter turns to the decomposition of the small diagonal and its application to the topology of families. Finally, the chapter discusses integral coefficients and birational invariants before providing a brief overview of the following chapters.

Keywords:   cohomology, Chow groups, smooth projective varieties, generalized Bloch conjecture, small diagonal, integral coefficients, birational invariants

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