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Derived Categories of Surfaces

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter completes the classification of algebraic surfaces from the point of view of their derived categories. Abelian, K3, and elliptic surfaces play a special role. For all other surfaces, the ... More


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


On the Chow ring of <i>K3</i> surfaces and hyper-Kahler manifolds

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/9780691160504.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter considers varieties whose Chow ring has special properties. This includes abelian varieties, K3 surfaces, and Calabi–Yau hypersurfaces in projective space. For K3 surfaces S, it was ... More


Maps, Sheaves and <i>K</i>3 Surfaces

Rahul Pandharipande

in Lectures on Geometry

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.003.0005
Subject:
Mathematics, Geometry / Topology

The conjectural equivalence of curve counting on Calami- Yau 3-folds via stable maps and stable pairs is discussed. By considering Cali-Yau 3-folds with K3 fibrations, the correspondence naturally ... More


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 Geometry

Edward Witten, Martin Bridson, Helmut Hofer, Marc Lackenby, and Rahul Pandharipande

N M J Woodhouse (ed.)

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.001.0001
Subject:
Mathematics, Geometry / Topology

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, ... More


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