Seminar| Institute of Mathematical Sciences
Time: Thursday, November 28th, 2024,14:30-15:30
Location: IMS, RS408
Speaker:Hanfei Guo, SCMS Fudan University
Abstract:In 1999, Verbitsky introduced the concept of hyperholomorphic vector bundles on higher-dimensional hyper-Kähler manifolds. Despite their good moduli properties that resemble those of simple sheaves on K3 surfaces, constructing examples beyond tangent bundles and their relatives is quite challenging. Recently, the notion of atomic sheaves, studied by Markman and Beckmann, has been helpful in this direction. In this talk, we provide new examples of atomic sheaves on an infinite series of families of projective hyper-Kähler manifolds. Furthermore, after applying derived equivalences and deformations, we construct (projectively) hyperholomorphic bundles on any hyper-Kähler manifold of $K3^{[n]}$-type for infinitely many $n$. This is based on joint work with Zhiyu Liu.