Person: Logares Jiménez, Marina Lucía
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First Name
Marina Lucía
Last Name
Logares Jiménez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Álgebra, Geometría y Topología
Area
Geometría y Topología
Identifiers
4 results
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Now showing 1 - 4 of 4
Item Brauer group of moduli spaces of pairs(Communications in Algebra, 2012) Biswas, Indranil; Logares Jiménez, Marina Lucía; Vicente Muñoz, Gerardo DeWe show that the Brauer group of the moduli space of stable pairs with fixed determinant over a curve is zero.Item Rationality of the moduli space of stable pairs over a complex curve(Nonlinear Analysis:Stability, Approximation, and Inequalities, 2012) Biswas, Indranil; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente; Pardalos, Panos M.; Georgiev, Pando G.; Srivastava, Hari M.Let X be a smooth complex projective curve of genus g≥2. A pair on X is formed by a vector bundle E→X and a global non-zero section ϕ∈H 0(E). There is a concept of stability for pairs depending on a real parameter τ, giving rise to moduli spaces of τ-stable pairs of rank r and fixed determinant Λ. In this paper, we prove that the moduli spaces are in many cases rational.Item Hodge polynomials of SL (2,C)-character varieties for curves of small genus(Revista matemática complutense, 2013) Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente; Newstead, P. E.We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve into for the case of small genus and allowing the holonomy around a fixed point to be any matrix of that is diagonalisable, or of either of the two Jordan types. For this, we introduce a new geometric technique, based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrationsItem Hodge polynomials of the SL(2, C)-character variety of an elliptic curve with two marked points(International journal of mathematics, 2014) Logares Jiménez, Marina Lucía; Muñoz Velázquez, VicenteWe compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, C). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.