We define the notion of generalized logarithmic sheaves on a smooth projective surface, associated to a pair consisting of a reduced curve and some fixed points on it. We then set up the study of the Torelli property in this setting, focusing mostly in the case of the blow-up of the projective plane on a reduced set of points and, in particular, in the case of the cubic surface. We also study the stability property of generalized logarithmic sheaves as well as carrying out the description of their moduli spaces.

Generalized Logarithmic Sheaf on Smooth Projective Surfaces / Huh, S.; Marchesi, S; PONS LLOPIS, JUAN FRANCISCO; Vallès, Jean. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2023:21(2023), pp. 18387-18442. [10.1093/imrn/rnad029]

Generalized Logarithmic Sheaf on Smooth Projective Surfaces

Juan Francisco Pons Llopis;
2023

Abstract

We define the notion of generalized logarithmic sheaves on a smooth projective surface, associated to a pair consisting of a reduced curve and some fixed points on it. We then set up the study of the Torelli property in this setting, focusing mostly in the case of the blow-up of the projective plane on a reduced set of points and, in particular, in the case of the cubic surface. We also study the stability property of generalized logarithmic sheaves as well as carrying out the description of their moduli spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2978597