Diagonal property of the symmetric product of a smooth curve

Biswas, Indranil; Singh, Sanjay Kumar

doi:10.1016/j.crma.2015.02.007

Algebraic geometry

Diagonal property of the symmetric product of a smooth curve
[Propriété de la diagonale pour les produits symétriques d'une courbe lisse]

Présenté par : Claire Voisin

Biswas, Indranil ¹ ; Singh, Sanjay Kumar 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

Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 445-448.

Résumé
Abstract

Soit C une courbe irréductible, lisse, définie sur un corps algébriquement clos. Nous montrons que le produit symétrique ${Sym}^{d} (C)$ a la propriété de la diagonale, pour tout $d \geq 1$ . Pour tous entiers n et r, soit $Q_{O_{C}^{\oplus n}} (n r)$ le schéma Quot paramétrant tous les quotients de torsion de $O_{C}^{\oplus n}$ de degré nr. Nous montrons que $Q_{O_{C}^{\oplus n}} (n r)$ a la propriété du point, faible.

Let C be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product ${Sym}^{d} (C)$ has the diagonal property for all $d \geq 1$ . For any positive integers n and r, let $Q_{O_{C}^{\oplus n}} (n r)$ be the Quot scheme parameterizing all the torsion quotients of $O_{C}^{\oplus n}$ of degree nr. We prove that $Q_{O_{C}^{\oplus n}} (n r)$ has the weak-point property.

Reçu le : 2015-01-14
Accepté le : 2015-02-25
Publié le : 2015-03-11

DOI : 10.1016/j.crma.2015.02.007

Affiliations des auteurs :

Biswas, Indranil ¹ ; Singh, Sanjay Kumar 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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Biswas, Indranil; Singh, Sanjay Kumar. Diagonal property of the symmetric product of a smooth curve. Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 445-448. doi : 10.1016/j.crma.2015.02.007. http://www.numdam.org/articles/10.1016/j.crma.2015.02.007/

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Cité par Sources :

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