Nef cones of some Quot schemes on a Smooth Projective Curve

Chandranandan Gangopadhyay; Ronnie Sebastian

doi:10.5802/crmath.245

Géométrie algébrique

Nef cones of some Quot schemes on a Smooth Projective Curve

Chandranandan Gangopadhyay ¹ ; Ronnie Sebastian ¹

¹ Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India.

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

Résumé

Let $C$ be a smooth projective curve over $ℂ$ . Let $n, d \geq 1$ . 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 $n \geq d$ 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.

Reçu le : 2021-02-26
Accepté le : 2021-07-13
Accepté après révision le : 2021-07-16
Publié le : 2021-10-08

DOI : 10.5802/crmath.245

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

Affiliations des auteurs :

Chandranandan Gangopadhyay ¹ ; Ronnie Sebastian ¹

¹ Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     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},
}

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Chandranandan Gangopadhyay; Ronnie Sebastian. Nef cones of some Quot schemes on a Smooth Projective Curve. Comptes Rendus. Mathématique, Volume 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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