Perverse sheaves on symmetric products of the plane

Autor:	Braden, Tom, Mautner, Carl
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	For any field $k$, we give an algebraic description of the category $\mathrm{Perv}_\mathscr{S}(S^n (\mathbb{C}^2),k)$ of perverse sheaves on the $n$-fold symmetric product of the plane $S^n(\mathbb{C}^2)$ constructible with respect to its natural stratification and with coefficients in $k$. In particular, we show that it is equivalent to the category of modules over a new algebra that is closely related to the Schur algebra. As part of our description we obtain an analogue of modular Springer theory for the Hilbert scheme $\mathrm{Hilb}^n(\mathbb{C}^2)$ of $n$ points in the plane with its Hilbert-Chow morphism. Comment: 50 pages. Added some clarifications and made minor corrections
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.14351 Zobrazit plný text záznamu View this record from Arxiv