On the compactified Kobayashi-Hitchin map
报告题目(Title)：On the compactified Kobayashi-Hitchin map
报告人(Speaker)：何思奇 （中科院晨兴数学中心）
地点(Place)：后主楼1220
时间(Time)：2023年3月31日 16:00-17:00
邀请人(Inviter)：田垠
报告摘要
The Kobayashi-Hitchin correspondence identifies the Dolbeault moduli space of SL(2,C) Higgs bundles with the Hitchin moduli space of solutions to the SU(2) self-duality equations over a smooth projective curve. While the Dolbeault moduli space admits a natural compactification via the C-star action, the Hitchin moduli space is compactified by limiting configurations to the decoupled Hitchin equations. Follows from the work of Mazzeo-Swoboda-Weiss-Witt and Mochizuki, one could define a map from the compactified Dolbeault moduli space to the compactified Hitchin moduli space. Surprisingly, we prove that this map is not injective, not surjective, and not even continuous with respect to the natural topology near the singular locus. This is joint work with R. Mazzeo, X. Na, and R. Wentworth.
