$K3^{[n]}$ -型流形的卡氏平方上的超全纯层的自然性
Naturality of the hyperholomorphic sheaf over the cartesian square of a manifold of $K3^{[n]}$-type
摘要：
设M是K ~ 3曲面S上稳定层的2n维光滑紧致模空间，U是S × M上的泛层.在M x M上存在秩为2n-2的自然自反层E，即U到M x S x M的两个拉回的第一个相对扩张层。我们证明了E关于M上的每个Kahler类是斜稳定的。已知层E变形为X × X上的层E'，对每个流形X变形等价于M，我们证明了E'关于X上的每个Kahler类是斜率稳定的。稳定舱结构的这种不重要性与S. Mehrotra和作者表明，变形层E'是典型的。因此，在我们早先关于S的工作中，与对（X × X，E '）相联系的预三角化K3范畴。Mehrotra仅依赖于X的同构类。
英文摘要：
Let M be a 2n-dimensional smooth and compact moduli space of stable sheaves on a K3 surface S and U a universal sheaf over S x M. Over M x M there exists a natural reflexive sheaf E of rank 2n-2, namely the first relative extension sheaf of the two pullbacks of U to M x S x M. We prove that E is slope-stable with respect to every Kahler class on M. The sheaf E is known to deform to a sheaf E' over X x X, for every manifold X deformation equivalent to M, and we prove that E' is slope-stable with respect to every Kahler class on X. This triviality of the stability chamber structure combines with a result of S. Mehrotra and the author to show that the deformed sheaf E' is canonical. Consequently, the pretriangulated K3 category associated to the pair (X x X,E') in our earlier work with S. Mehrotra depends only on the isomorphism class of X.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
