Nef cones of some Quot schemes on a Smooth Projective Curve

Gangopadhyay, Chandranandan; Sebastian, Ronnie

Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 999-1022.

Let $C$ be a smooth projective curve over $ℂ$. Let $n,d\ge 1$. Let $𝒬$ be the Quot scheme parameterizing torsion quotients of the vector bundle ${𝒪}_C^n$ 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 $n\ge d$ 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.

Classification : 14C05, 14C20, 14C22, 14E30, 14J10, 14J60

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