论文标题
theta组和Hyperkähler品种的投影模型
Theta groups and projective models of hyperkähler varieties
论文作者
论文摘要
We define the theta group associated to a simple coherent sheaf $\cal F$ on a hyperkähler manifold $X$ of Kummer type or OG6 type, provided $g^{*}({\cal F})$ is isomorphic to $\cal F$ for every automorphism $g$ of $X$ acting trivially on $H^2(X)$.请注意，如果$ \ cal f $可逆，如果$ \ cal f $是$ 4 $稳定的矢量捆绑包之一，则可以满足此条件。我们计算theta捆绑包的换向器配对，而等级$ 4 $ arxiv的模块化向量束：2203.03987（切线束的换向器配对是微不足道的）。我们是为了对Kummer（或OG6）类型的两极分化品种的本地完整家庭的明确描述进行明确描述。
We define the theta group associated to a simple coherent sheaf $\cal F$ on a hyperkähler manifold $X$ of Kummer type or OG6 type, provided $g^{*}({\cal F})$ is isomorphic to $\cal F$ for every automorphism $g$ of $X$ acting trivially on $H^2(X)$. Note that this condition is satisfied if $\cal F$ is invertible, if $\cal F$ is one of the rank $4$ stable vector bundles on general polarized HK fourfolds with certain discrete invariants constructed in arXiv:2203.03987, or if $\cal F$ is the tangent bundle. We compute the commutator pairings of theta groups of line bundles and the rank $4$ modular vector bundles of arXiv:2203.03987 (the commutator pairing of the tangent bundle is trivial). We have been motivated by the quest for an explicit description of locally complete families of polarized varieties of Kummer (or OG6) type.
