Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections
Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections
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全纯辛簇和单调反射的素例外因数
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发表时间：
2009
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通讯作者：
E. Markman
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作者：
E. Markman
设X是射影不可约全纯辛流形。X的第二整上同调是关于Beauville-Bogomolov配对的格。称X上的因子E为素例外因子，如果E是既约且不可约的，且具有负Beauville-Bogomolov度.
设E是X上的一个素例外因子。我们首先观察到，与E相关联的是X的积分上同调的单值对合，它作为E的上同调类的反射作用在第二上同调格上（定理1.1）。
然后，我们专门的情况下，X是变形相当于长度为n零维子计划的K3表面的希尔伯特计划。我们确定了X上例外因子类的集合（定理1.11）。这导致了X的可动锥的闭合的确定。
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.