Nef cones of some Quot schemes on a Smooth Projective Curve

Abstract

Let C be a smooth projective curve over C. Let n, d ≥ 1. Let Q be the Quot scheme parameterizing torsion quotients of the vector bundle O n C of degree d . In this article we study the nef cone of 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 Q to be nef.

Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points

“…Over other surfaces, related results can be found in [3,6,9,19,23,24,30,34,39], among others. The nef cones of divisors of the punctual Quot schemes of curves of genus 0 and 1 were determined in [15,36].…”