Year: 2021
Type: article
Abstract: We show that the Quot scheme Q n L = Quot A 3 (IL, n) parameterising length n quotients of the ideal sheaf of a line in A 3 is a global critical locus, and calculate the resulting motivic partition function (varying n), in the ring of relative motives over the configuration space of points in A 3 .As in the work of Behrend-Bryan-Szendrői, this enables us to define a virtual motive for the Quot scheme of n points of the ideal sheaf IC ⊂ OY , where C ⊂ Y is a smooth curve embedded in a smooth 3-fold Y , and we compute the associated motivic partition function.The result fits into a motivic wall-crossing type formula, refining the relation between Behrend's virtual Euler characteristic of Quot Y (IC , n) and of the symmetric product Sym n C. Our 'relative' analysis leads to results and conjectures regarding the pushforward of the sheaf of vanishing cycles along the Hilbert-Chow map Q n L → Sym n (A 3 ), and connections with cohomological Hall algebra representations.
DOI: 10.1112/jlms.12463
Authors: Ben Davison, Andrea T. Ricolfi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,000
OpenAlex ID: W2947064310