Nef cones of some Quot schemes on a smooth projective curve

2020/06/30 by Gangopadhyay, Chandranandan, Sebastian, Ronnie · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.16666

Abstract

Let C be a smooth projective curve over \mathbb C. Let n,d≥ 1. Let \mathcal Q be the Quot scheme parameterizing torsion quotients of the vector bundle \mathcal Oⁿ_C of degree d. In this article we study the nef cone of \mathcal Q. We give a complete description of the nef cone in the case of elliptic curves. We compute it in the case when d=2 and C very general, in terms of the nef cone of the second symmetric product of C. In the case when n≥ d and C very general, we give upper and lower bounds for the Nef cone. In general, we give a necessary and sufficient criterion for a divisor on \mathcal Q to be nef.

Cited by

• A Borel--Weil--Bott theorem for Quot schemes on ℙ¹

Related

• Nef and Effective cones of some Quot Schemes
• Some recent results on the punctual Quot schemes
• Infinitesimal deformations of some quot schemes, II
• Fundamental Group Schemes of some Quot Schemes on a smooth projective\n curve
• Nef cone and Seshadri constants on products of projective bundles over curves