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Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this ... 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


Decomposition of the Diagonal

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/9780691160504.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter explains the method initiated by Bloch and Srinivas, which leads to statements of the following: if a smooth projective variety has trivial Chow groups of k-cycles homologous to 0 for k ... More


Introduction to Variations of Hodge Structure

Eduardo Cattani

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/9780691161341.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter emphasizes the theory of abstract variations of Hodge structure (VHS) and, in particular, their asymptotic behavior. It first studies the basic correspondence between local systems, ... More


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