Surfaces on the Severi line
Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has K-S(2) >= 4 chi(O-S). We prove that the equality K-S(2) = 4 chi(O-S) holds if and only if q(S) := h(1)(Os) = 2 and the canonical model of S is a double cover of the Albanese surf...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/103930 |
| Acceso en línea: | https://hdl.handle.net/2117/103930 https://dx.doi.org/10.1016/j.matpur.2015.11.012 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic topology Linear systems Surfaces of general type Severi inequality Etale coverings Irregular varieties general type inequality varieties Topologia algebraica Sistemes lineals Classificació AMS::14 Algebraic geometry::14J Surfaces and higher-dimensional varieties Classificació AMS::14 Algebraic geometry::14E Birational geometry Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has K-S(2) >= 4 chi(O-S). We prove that the equality K-S(2) = 4 chi(O-S) holds if and only if q(S) := h(1)(Os) = 2 and the canonical model of S is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities. (C) 2015 Elsevier Masson SAS. All rights reserved. |
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