Algebraic geometry
Diagonal property of the symmetric product of a smooth curve
Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 445-448.

Let C be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product $Symd(C)$ has the diagonal property for all $d≥1$. For any positive integers n and r, let $QOC⊕n(nr)$ be the Quot scheme parameterizing all the torsion quotients of $OC⊕n$ of degree nr. We prove that $QOC⊕n(nr)$ has the weak-point property.

Soit C une courbe irréductible, lisse, définie sur un corps algébriquement clos. Nous montrons que le produit symétrique $Symd(C)$ a la propriété de la diagonale, pour tout $d≥1$. Pour tous entiers n et r, soit $QOC⊕n(nr)$ le schéma Quot paramétrant tous les quotients de torsion de $OC⊕n$ de degré nr. Nous montrons que $QOC⊕n(nr)$ a la propriété du point, faible.

Accepted:
Published online:
DOI: 10.1016/j.crma.2015.02.007

Indranil Biswas 1; Sanjay Kumar Singh 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
2 Institute of Mathematics, Polish Academy of Sciences, Warsaw, 00656, Poland
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Indranil Biswas; Sanjay Kumar Singh. Diagonal property of the symmetric product of a smooth curve. Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 445-448. doi : 10.1016/j.crma.2015.02.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.02.007/

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The first named author is supported by the J.C. Bose Fellowship. The second named author is supported by IMPAN Postdoctoral Research Fellowship.