Higher-dimensional Clifford-Severi equalities
Abstract.LetXbe a smooth complex projective variety,a:X¿Aa mor-phism to an abelian variety such that Pic0(A) injects into Pic0(X) and letLbe a line bundle onX; denote byh0a(X,L) the minimum ofh0(X,L¿a*a) fora¿Pic0(A). The so-called Clifford-Severi inequalities have been proven in [2]and [5]; in part...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/177538 |
| Acesso em linha: | https://hdl.handle.net/2117/177538 https://dx.doi.org/10.1142/S0219199719500792 |
| Access Level: | acceso abierto |
| Palavra-chave: | Algebraic geometry Irregular varieties Birational classification Clifford–Severi inequalities Geometria algebraica Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes Classificació AMS::14 Algebraic geometry::14J Surfaces and higher-dimensional varieties Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | Abstract.LetXbe a smooth complex projective variety,a:X¿Aa mor-phism to an abelian variety such that Pic0(A) injects into Pic0(X) and letLbe a line bundle onX; denote byh0a(X,L) the minimum ofh0(X,L¿a*a) fora¿Pic0(A). The so-called Clifford-Severi inequalities have been proven in [2]and [5]; in particular, for anyLthere is a lower bound for the volume givenby:vol(L)=n!h0a(X,L),and, ifKX-Lis pseudoeffective,vol(L)=2n!h0a(X,L).In this paper we characterize varieties and line bundles for which the aboveClifford-Severi inequalities are equalities |
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