Joyce's invariant and Virasoro Constraints for Quot schemes on curves
Abstract
Let be a smooth projective curve over and let be a vector bundle over . Let denote the Quot scheme which parametrizes quotients of of rank and degree . Following Joyce's recipe [Joy21], we introduce Joyce's enumerative invariant for the Quot scheme . The invariant can be viewed as a generalization of the virtual fundamental cycle of the Quot scheme. We evaluate intersection pairings on the Quot scheme by computing its invariant explicitly. Following the reformulation of sheaf-theoretic Virasoro constraints in terms of Joyce's vertex algebra framework in [BLM24], we give a proof of the Virasoro constraints for the Quot scheme . With the help of these constraints, we compute the (virtual) intersection numbers of -classes on the Quot schemes.
Cite
@article{arxiv.2608.04795,
title = {Joyce's invariant and Virasoro Constraints for Quot schemes on curves},
author = {Parvez Rasul},
journal= {arXiv preprint arXiv:2608.04795},
year = {2026}
}
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