Hodge polynomials of the moduli spaces of triples of rank (2,2).

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this pap...

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Detalhes bibliográficos
Autores: Muñoz, Vicente, Ortega, Daniel, Vázquez Gallo, M. Jesús
Tipo de documento: artigo
Data de publicação:2009
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/50580
Acesso em linha:https://hdl.handle.net/20.500.14352/50580
Access Level:Acceso aberto
Palavra-chave:512.7
Moduli space
Complex curve
Stable triple
Hodge polynomial.
Geometria algebraica
1201.01 Geometría Algebraica
Descrição
Resumo:Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E1) = rk(E2) = 2, using the theory of mixed Hodge structures (in the cases that they are smooth and compact). This gives in particular the Poincar´e polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.