Person:
Logares Jiménez, Marina Lucía

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First Name
Marina Lucía
Last Name
Logares Jiménez
URI
https://hdl.handle.net/20.500.14352/75671
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Álgebra, Geometría y Topología
Area
Geometría y Topología
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2012 - 201922020 - 20233
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Now showing 1 - 5 of 5
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    Stratification of SU(r)-character varieties of twisted Hopf links
    (2023) González-Prieto, Ángel; Logares Jiménez, Marina Lucía; Martínez, Javier; Muñoz, Vicente
    We describe the geometry of the character variety of representations of the fundamental group of the complement of a Hopf link with n twists, namely Γn=⟨x,y|[xn,y]=1⟩ into the group SU(r). For arbitrary rank, we provide geometric descriptions of the loci of irreducible and totally reducible representations. In the case r=2, we provide a complete geometric description of the character variety, proving that this SU(2)-character variety is a deformation retract of the larger SL(2,C)-character variety, as conjectured by Florentino and Lawton. In the case r=3, we also describe different strata of the SU(3)-character variety according to the semi-simple type of the representation.
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    Brauer group of moduli spaces of pairs
    (Communications in Algebra, 2012) Biswas, Indranil; Logares Jiménez, Marina Lucía; Vicente Muñoz, Gerardo De
    We show that the Brauer group of the moduli space of stable pairs with fixed determinant over a curve is zero.
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    Motive of the representation varietes of torus knots for low rank affine groups
    (2022) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente
    We 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].
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    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.
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    Representation Variety for the Rank One Affine Group
    (Mathematical Analysis in Interdisciplinary Research, 2021) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente
    The 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.