Comptes Rendus
Algebraic geometry
Nef cones of some Quot schemes on a Smooth Projective Curve
Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 999-1022.

Let C be a smooth projective curve over . Let n,d1. 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 nd 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.

Revised after acceptance:
Published online:
DOI: 10.5802/crmath.245
Classification: 14C05, 14C20, 14C22, 14E30, 14J10, 14J60

Chandranandan Gangopadhyay 1; Ronnie Sebastian 1

1 Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     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},
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     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.

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