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

Claire Voisin

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.001.0001
Subject:
Mathematics, Geometry / Topology

This book 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. ... More


Lectures on Algebraic Cycles and Chow Groups

Jacob Murre

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)

in Hodge Theory (MN-49)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter showcases five lectures on algebraic cycles and Chow groups. The first two lectures are over an arbitrary field, where they examine algebraic cycles, Chow groups, and equivalence ... More


Introduction

Claire Voisin

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

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.003.0001
Subject:
Mathematics, Geometry / Topology

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 ... More


Hodge Theory (MN-49)

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The ... More


Review of Hodge theory and algebraic cycles

Claire Voisin

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

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter provides the background for the studies to be undertaken in succeeding chapters. It reviews Chow groups, correspondences and motives on the purely algebraic side, cycle classes, and ... More


The Spread Philosophy in the Study of Algebraic Cycles

Mark L. Green

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)

in Hodge Theory (MN-49)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.003.0010
Subject:
Mathematics, Geometry / Topology

This chapter discusses the spread philosophy in the study of algebraic cycles, in order to make use of a geometry by considering a variation of Hodge structure where D is the Hodge domain (or the ... More


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