Involutions and linear systems on holomorphic symplectic manifolds
Involutions and linear systems on holomorphic symplectic manifolds
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全纯辛流形上的对合和线性系统
DOI：
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发表时间：
2004
期刊：
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通讯作者：
K. O’Grady
中科院分区：
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作者：
K. O’Grady
具有自交因子2的K3曲面是在六次曲线上分支的平面的双重覆盖。我们推测，类似的说法也适用于一般偶(X，H)，其中X是(K3)[n]的变形，H是Beauville二次型的平方2的充分因子。如果n=2，则根据猜想，X是奇异的)六次4重覆盖的重覆盖
$$mathbb{P}^{5}.$$它源于这样的猜想：(K3)[n]的变形带有一个2次因子(不一定充分)，它有一个反辛双调对合。我们检验了这个猜想。在这样做的过程中，我们遇到了一些有趣的几何：两个反辛对合生成一个有趣的动力系统的例子，一个奇异对偶的例子，以及可能是模空间-2次拟极化(X，H)的对合的例子，其中X是(K3)[2]的变形。
Abstract.A K3 surface with an ample divisor of self-intersection 2 is a double cover of the plane branched over a sextic curve. We conjecture that similar statement holds for the generic couple (X, H) with X a deformation of (K3)[n] and H an ample divisor of square 2 for Beauville’s quadratic form. If n = 2 then according to the conjecture X is a double cover of a singular) sextic 4-fold in
$$mathbb{P}^{5} .$$ It follows from the conjecture that a deformation of (K3)[n] carrying a divisor (not necessarily ample) of degree 2 has an anti-symplectic birational involution. We test the conjecture. In doing so we bump into some interesting geometry: examples of two antisymplectic involutions generating an interesting dynamical system, a case Strange duality and what is probably an involution on the moduli space degree-2 quasi-polarized (X, H) where X is a deformation of (K3)[2].