A short way of counting maps to hypersurfaces in Grassmannians
Algebraic Geometry
2025-06-13 v1
Abstract
Using a Quot scheme compactification, we calculate the virtual count of maps of degree from a smooth projective curve of genus to a hypersurface in a Grassmannian, sending specified points of the curve to special Schubert subvarieties restricted to the hypersurface. We study the question of whether this virtual count is in fact enumerative under suitable conditions on the hypersurface, in the regime when the map degree is large.
Cite
@article{arxiv.2506.10593,
title = {A short way of counting maps to hypersurfaces in Grassmannians},
author = {Alina Marian and Shubham Sinha},
journal= {arXiv preprint arXiv:2506.10593},
year = {2025}
}