Open Access
Summer 2013 Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections
Eyal Markman
Kyoto J. Math. 53(2): 345-403 (Summer 2013). DOI: 10.1215/21562261-2081243


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 H(X,Z), which acts on the second cohomology lattice as the reflection by the cohomology class [E] of E.

We then specialize to the case where X is deformation equivalent to the Hilbert scheme of length n zero-dimensional subschemes of a K3 surface, n2. We determine the set of classes of exceptional divisors on X. This leads to a determination of the closure of the movable cone of X.


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Eyal Markman. "Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections." Kyoto J. Math. 53 (2) 345 - 403, Summer 2013.


Published: Summer 2013
First available in Project Euclid: 20 May 2013

zbMATH: 1271.14016
MathSciNet: MR3079308
Digital Object Identifier: 10.1215/21562261-2081243

Primary: 14D05 , 14J60
Secondary: 14C20 , 14J28 , 53C26

Rights: Copyright © 2013 Kyoto University

Vol.53 • No. 2 • Summer 2013
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