Hyperquot schemes on curves: virtual class and motivic invariants

Autor:	Monavari, Sergej, Ricolfi, Andrea T.
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	Let $C$ be a smooth projective curve, $E$ a locally free sheaf. Hyperquot schemes on $C$ parametrise flags of coherent quotients of $E$ with fixed Hilbert polynomial, and offer alternative compactifications to the spaces of maps from $C$ to partial flag varieties. Motivated by enumerative geometry, in this paper we construct a perfect obstruction theory (and hence a virtual class and a virtual structure sheaf) on these moduli spaces, which we use to provide criteria for smoothness and unobstructedness. Under these assumptions, we determine their motivic partition function in the Grothendieck ring of varieties, in terms of the motivic zeta function of $C$. Comment: 37 pages. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.17942 Zobrazit plný text záznamu View this record from Arxiv