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Speaker:

Shengxuan Liu
Affiliation:

University of Michigan/MPIM
Date:

Thu, 04/07/2024 - 10:30 - 12:00
Location:

MPIM Lecture Hall
Parent event:

Seminar Algebraic Geometry (SAG) In this talk, I will discuss some properties of spherical bundles on K3 surfaces. Let S be a K3 surface with the bounded derived category D^b(S). Let E be a spherical object in D^b(S). Then there always exists a non-zero object F satisfying RHom(E,F)=0. Further, there exists a spherical bundle E on some K3 surfaces that is unstable with respect to all polarization on S. If time permits, I will also discuss a way to “count” spherical bundles with a fixed Mukai vector. These provide (partial) answers to some questions of Huybrechts. This is a joint work with Chunyi Li.

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