Nef cones of some Quot schemes on a smooth projective curve
Chandranandan Gangopadhyay, Ronnie Sebastian

TL;DR
This paper investigates the nef cone of Quot schemes on smooth projective curves, providing explicit descriptions for elliptic curves and bounds in general, linking to symmetric products and establishing nef criteria.
Contribution
It offers a complete description of the nef cone for elliptic curves and bounds for general cases, connecting nef cones of Quot schemes to symmetric products of curves.
Findings
Complete nef cone description for elliptic curves
Bounds for nef cone when $n \,\geq\, d$ and $C$ very general
Necessary and sufficient nef criterion for divisors on Quot schemes
Abstract
Let be a smooth projective curve over . Let . Let be the Quot scheme parameterizing torsion quotients of the vector bundle of degree . In this article we study the nef cone of . We give a complete description of the nef cone in the case of elliptic curves. We compute it in the case when and very general, in terms of the nef cone of the second symmetric product of . In the case when and 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 to be nef.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
