论文标题
尺寸六
Supersingular O'Grady varieties of dimension six
论文作者
论文摘要
奥格雷迪（O'Grady）通过在阿伯利亚表面上以某些模量为稳定的滑轮的模量空间来构建了一个6维的不可塑态象征性品种。在本文中，我们自然地将O'Grady的构造扩展到了阳性P大于2的田地，称为OG6品种。我们表明，超级OG6品种是Urirational的，其合理的共同体学组是由代数类别产生的，其合理的Chow动机是泰特类型的。在这种情况下，这些结果证实了普遍的Artin- shioda猜想，超级泰特猜想和我们先前工作中提出的超级bloch猜想，类似于Supellingular K3表面的理论。
O'Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this paper, we naturally extend O'Grady's construction to fields of positive characteristic p greater than 2, called OG6 varieties. We show that a supersingular OG6 variety is unirational, its rational cohomology group is generated by algebraic classes, and its rational Chow motive is of Tate type. These results confirm in this case the generalized Artin--Shioda conjecture, the supersingular Tate conjecture and the supersingular Bloch conjecture proposed in our previous work, in analogy with the theory of supersingular K3 surfaces.
