题目：Sheaves on Non-Reduced Curves in a Projective Surface

报告人：袁瑶 教授 (首都师范大学)

地点：腾讯会议室

时间：2021年12月17日（星期五） 9:45-10:45

摘要: Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface, and moduli spaces of Higgs bundles as well. We estimate the dimension of the stack M_X(nC, \chi) of pure sheaves supported at the non-reduced curve nC (n ≥ 2) with C an integral curve on X. We prove that the Hilbert-Chow morphism h_{L,\chi} : M_X^H(L, \chi) → |L| sending each semistable 1-dimensional sheaf to its support have all its fibers of the same dimension for X Fano or with trivial canonical line bundle and |L| contains integral curves.  The strategy is to firstly deal with the case with C smooth and then do induction on the arithmetic genus of C which once can decrease by a blow-up given C singular.  As an application, we generalize the result of Maulik-Shen on the cohomology \chi-independence of M_X^H(L,\chi) to X any del Pezzo surface not necessarily toric.

腾讯会议：383-5163-6649

会议密码：202112

会议链接：https://meeting.tencent.com/dm/7x2K1cFJsUpl

欢迎各位参加！