中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

代数几何研讨班

Speaker: 高烁（Stony Brook University）

Inviter: 刘杰

Language:Chinese

Title: Decompositions of modular perverse sheaves on symmetric products of the plane

Time&Venue: 2025年9月16日（星期二）10:30-11:30& MCM 410

Abstract: Fogarty's theorem tells us that Hilbert scheme of points of a smooth algebraic surface is a smooth variety, making Hilbert-Chow morphism in this case a very well-studied crepant resolution. Being a semi-small map, the Hilbert-Chow morphism often serves as an example for computation involving the celebrated decomposition theorem for perverse sheaves. However, if we allow the local systems to have (wild) positive characteristic, the decomposition theorem fails; but we can still decompose the pushforward of constant sheaf manually using Deligne's construction. This talk will focus on this manual decomposition and its interesting, close relation with the decomposition matrix of modular representation of permutation groups.