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Moving and Ample Cones of Holomorphic Symplectic Fourfolds

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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.

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Authors and Affiliations

  1. Department of Mathematics, Rice University, 6100 S. Main St., Houston, TX, 77251-1892, USA

    Brendan Hassett

  2. Courant Institute of Mathematical Sciences, NYU, 251 Mercer St., New York, NY, 10012, USA

    Yuri Tschinkel

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  1. Brendan Hassett
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  2. Yuri Tschinkel
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Correspondence to Brendan Hassett.

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Hassett, B., Tschinkel, Y. Moving and Ample Cones of Holomorphic Symplectic Fourfolds. Geom. Funct. Anal. 19, 1065–1080 (2009). https://doi.org/10.1007/s00039-009-0022-6

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  • DOI: https://doi.org/10.1007/s00039-009-0022-6

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