Title: A twisted derived category of hyper-Kähler varieties of $K3^{[n]}$-type Show Chinese title

Title: 超凯勒簇的扭曲导出范畴$K3^{[n]}$-型

Abstract: We conjecture that a natural twisted derived category of any hyper-K\"ahler variety of $K3^{[n]}$-type is controlled by its Markman-Mukai lattice. We prove the conjecture under numerical constraints, and our proof relies heavily on Markman's projectively hyperholomorphic bundle and a recently proven twisted version of the D-equivalence conjecture. In particular, we prove that any two fine moduli spaces of stable sheaves on a $K3$ surface are derived equivalent if they have the same dimension. Show Chinese abstract

Abstract: 我们猜想，任何类型为$K3^{[n]}$的超凯勒簇的自然扭转导出范畴都由其 Markman-Mukai 格子控制。 我们在数值限制下证明了这一猜想，并且我们的证明大量依赖于 Markman 的射影超全纯束以及最近证明的扭转版本的 D-等价猜想。 特别是，我们证明了如果两个稳定层模空间具有相同的维数，则它们在类型为$K3$的面上是导出等价的。