Person: Muñoz Velázquez, Vicente
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First Name
Vicente
Last Name
Muñoz Velázquez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Geometría y Topología
Identifiers
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Item Motive of the representation varietes of torus knots for low rank affine groups(2022) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, VicenteWe compute the motive of the variety of representations of the torus knot of type (m, n) into the affine groups AGL1(C) and AGL2(C). For this, we stratify the varieties and show that the motives lie in the subring generated by the Lefschetz motive q = [C].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 Representation Variety for the Rank One Affine Group(Mathematical Analysis in Interdisciplinary Research, 2021) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, VicenteThe aim of this chapter is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the representation variety into simpler pieces; the arithmetic method, focused on counting their number of points over finite fields; and the quantum method, which performs the computation by means of a Topological Quantum Field Theory. We also discuss the corresponding moduli spaces of representations and character varieties, which turn out to be non-equivalent due to the non-reductiveness of the underlying group.