论文标题
Hyperkähler的Kummer类型四倍的4稳定矢量束
Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type
论文作者
论文摘要
我们部分扩展到Hyperkähler四倍的Kummer类型，我们证明了有关HyperKähler（HK）类型$ K3^{[n]} $的稳定刚性向量捆绑包的结果。令$（m，h）$成为一般两极化的kummer类型的四倍，以便$ q_m（h）\ equiv -6 \ pmod {16} $，$ h $的划分为$ 2 $，或$ q_m（h）\ equiv -6 \ equiv -6 \ pmod {144} $，以及$ h $ h $ 6 $ 6 $ 6 $ 6 $ 6 $ 6 $ 6 $。我们表明，存在$ m $上的唯一（达到同构）坡度稳定矢量束$ \ cal f $，以便$ r（{\ cal f}）= 4 $，$ c_1（{\ cal f}）= h $，$Δ（{\ cal f}）= c_2（m）$。而且，$ \ cal f $是刚性的。我们的动机之一是渴望明确描述一个本地完整的kummer类型的四方面四倍的家族。
We partially extend to hyperkähler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperkähler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer type such that $q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, or $q_M(h)\equiv -6\pmod{144}$ and the divisibility of $h$ is $6$. We show that there exists a unique (up to isomorphism) slope stable vector bundle $\cal F$ on $M$ such that $r({\cal F})=4$, $ c_1({\cal F})=h$, $Δ({\cal F})=c_2(M)$. Moreover $\cal F$ is rigid. One of our motivations is the desire to describe explicitly a locally complete family of polarized HK fourfolds of Kummer type.
