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An update on the Riemann-Roch and Brill-Noether problems over surfaces

组织者

范祐维

演讲者

Yingbang Lin

时间

2025年04月16日 13:30 至 15:30

地点

A3-2-303

线上

Zoom 815 762 8413 (BIMSA)

摘要

We try to bound the dimension of the global sections of semistable sheaves in terms of the rank and the first Chern class. This improves the explicit Le Potier-Simpson bound when the first Chern class is small compared to the rank. In some cases, we also obtain the asymptotic bound as the second Chern class goes to infinity, using Bridgeland stability conditions. Understanding these bounds is the foundation of the Brill-Noether problem. Over K3 surfaces of Picard number one, we show examples of Brill-Noether loci which are non-empty and irreducible of expected dimensions. Besides their fundamental importance, we are also motivated by the Verlinde/Segre correspondence over surfaces. This is work in progress jointly with Thomas Goller and Zhixian Zhu.