Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections
By E. Markman. 2009
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Let X be a projective irreducible holomorphic symplectic manifold. The second integral cohomology of X is a lattice with respect to the Beauville-Bogomolov pairing. A divisor E on X is called a prime exceptional divisor, if E is reduced and irreducible and of negative Beauville-Bogomolov degree. Let E be a prime exceptional divisor on X. We first observe that associated to E is a monodromy involution of the integral cohomology of X, which acts on the second cohomology lattice as the reflection by the cohomology class of E (Theorem 1.1). We then specialize to the case that X is deformation equivalent to the Hilbert scheme of length n zero-dimensional subschemes of a K3 surface. We determine the set of classes of exceptional divisors on X (Theorem 1.11). This leads to a determination of the closure of the movable cone of X.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dcac9316d2539e0f1c98e16cbe4c291e06d59184
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- A note on the Kähler and Mori cones of hyperkähler manifolds (2015, methodology): “For the closure of the birational Kähler cone this numerical characterization has been given by Markman [12], we summarize it in Theorem 2.”