Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

David Harvey, Brendan Hassett, Yuri Tschinkel

Research output: Contribution to journalArticle

Abstract

We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic-symplectic manifolds, up to the action of the monodromy group. This paper addresses the case of manifolds deformation-equivalent to the Hilbert scheme of length-3 subschemes of a K3 surface. The class of the projective space in the cohomology ring has prescribed intersection properties, which translate into Diophantine equations. Possible homology classes correspond to integral points on an explicit elliptic curve; our proof entails showing that the only such point is two-torsion.

Original languageEnglish (US)
Pages (from-to)264-286
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number2
DOIs
StatePublished - Feb 2012

Fingerprint

Hilbert Scheme
K3 Surfaces
Projective Space
Torsional stress
Homology
Monodromy Group
Integral Points
Cohomology Ring
Symplectic Manifold
Diophantine equation
Elliptic Curves
Torsion
Intersection
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces. / Harvey, David; Hassett, Brendan; Tschinkel, Yuri.

In: Communications on Pure and Applied Mathematics, Vol. 65, No. 2, 02.2012, p. 264-286.

Research output: Contribution to journalArticle

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