Let be a projective irreducible holomorphic symplectic manifold. The second integral cohomology of is a lattice with respect to the Beauville–Bogomolov pairing. A divisor on is called a prime exceptional divisor if is reduced and irreducible and of negative Beauville–Bogomolov degree.
Let be a prime exceptional divisor on . We first observe that associated to is a monodromy involution of the integral cohomology , which acts on the second cohomology lattice as the reflection by the cohomology class of .
We then specialize to the case where is deformation equivalent to the Hilbert scheme of length zero-dimensional subschemes of a surface, . We determine the set of classes of exceptional divisors on . This leads to a determination of the closure of the movable cone of .
"Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections." Kyoto J. Math. 53 (2) 345 - 403, Summer 2013. https://doi.org/10.1215/21562261-2081243