Moving and ample cones of holomorphic symplectic fourfolds

Brendan Hassett; Yuri Tschinkel

doi:10.1007/s00039-009-0022-6

Moving and ample cones of holomorphic symplectic fourfolds

Brendan Hassett, Yuri Tschinkel

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for ampleness of divisors on fourfolds deformation-equivalent to punctual Hilbert schemes of K3 surfaces.

Original language	English (US)
Pages (from-to)	1065-1080
Number of pages	16
Journal	Geometric and Functional Analysis
Volume	19
Issue number	4
DOIs	https://doi.org/10.1007/s00039-009-0022-6
State	Published - Dec 2009

Keywords

Ample cones
Birational geometry
Punctual Hilbert schemes of K3 surfaces

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/s00039-009-0022-6

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title = "Moving and ample cones of holomorphic symplectic fourfolds",

abstract = "We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for ampleness of divisors on fourfolds deformation-equivalent to punctual Hilbert schemes of K3 surfaces.",

keywords = "Ample cones, Birational geometry, Punctual Hilbert schemes of K3 surfaces",

author = "Brendan Hassett and Yuri Tschinkel",

note = "Funding Information: Acknowledgments. We are grateful to Daniel Huybrechts and Dmitry Kaledin for valuable conversations. The first author was partially supported by National Science Foundation Grants 0554491 and 0134259. He appreciates the hospitality of the University of G{\"o}ttingen. The second author was partially supported by National Science Foundation Grants 0554280 and 0602333.",

year = "2009",

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doi = "10.1007/s00039-009-0022-6",

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AU - Hassett, Brendan

AU - Tschinkel, Yuri

N1 - Funding Information: Acknowledgments. We are grateful to Daniel Huybrechts and Dmitry Kaledin for valuable conversations. The first author was partially supported by National Science Foundation Grants 0554491 and 0134259. He appreciates the hospitality of the University of Göttingen. The second author was partially supported by National Science Foundation Grants 0554280 and 0602333.

PY - 2009/12

Y1 - 2009/12

N2 - We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for ampleness of divisors on fourfolds deformation-equivalent to punctual Hilbert schemes of K3 surfaces.

AB - We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for ampleness of divisors on fourfolds deformation-equivalent to punctual Hilbert schemes of K3 surfaces.

KW - Ample cones

KW - Birational geometry

KW - Punctual Hilbert schemes of K3 surfaces

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 4

ER -

Moving and ample cones of holomorphic symplectic fourfolds

Abstract

Keywords

ASJC Scopus subject areas

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