Diagonal property of the symmetric product of a smooth curve
Comptes Rendus Mathematique, ISSN: 1631-073X, Vol: 353, Issue: 5, Page: 445-448
2015
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S1631073X15000606; http://dx.doi.org/10.1016/j.crma.2015.02.007; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84928056857&origin=inward; https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.02.007/; https://dx.doi.org/10.1016/j.crma.2015.02.007
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