Géométrie algébrique
Nef cones of some Quot schemes on a Smooth Projective Curve
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.

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DOI : https://doi.org/10.5802/crmath.245
Classification : 14C05,  14C20,  14C22,  14E30,  14J10,  14J60
@article{CRMATH_2021__359_8_999_0,
author = {Chandranandan Gangopadhyay and Ronnie Sebastian},
title = {Nef cones of some {Quot} schemes on a {Smooth} {Projective} {Curve}},
journal = {Comptes Rendus. Math\'ematique},
pages = {999--1022},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {8},
year = {2021},
doi = {10.5802/crmath.245},
language = {en},
}
Chandranandan Gangopadhyay; Ronnie Sebastian. Nef cones of some Quot schemes on a Smooth Projective Curve. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 999-1022. doi : 10.5802/crmath.245. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.245/

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