Comptes Rendus
Analytic geometry
Quot schemes and Ricci semipositivity
[Schéma quot et semi-positivité de Ricci]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 577-581.

Soit X une surface de Riemann compacte et connexe de genre au moins deux, et soit QX(r,d) le schéma quot qui paramétrise tous les quotients torsion cohérents de OXr de degré d. L'espace QX(r,d) est aussi un espace de modules de vortex sur X. Nous démontrons que le fibré anticanonique de X n'a pas la propriété nef. De façon équivalente, QX(r,d) n'admet aucune métrique kählérienne dont la courbure de Ricci soit semi-positive.

Let X be a compact connected Riemann surface of genus at least two, and let QX(r,d) be the quot scheme that parameterizes all the torsion coherent quotients of OXr of degree d. This QX(r,d) is also a moduli space of vortices on X. Its geometric properties have been extensively studied. Here we prove that the anticanonical line bundle of QX(r,d) is not nef. Equivalently, QX(r,d) does not admit any Kähler metric whose Ricci curvature is semipositive.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2017.03.012

Indranil Biswas 1 ; Harish Seshadri 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Indian Institute of Science, Department of Mathematics, Bangalore 560003, India
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Indranil Biswas; Harish Seshadri. Quot schemes and Ricci semipositivity. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 577-581. doi : 10.1016/j.crma.2017.03.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.03.012/

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