Now showing items 1-6 of 6

    • A brief survey of Higgs bundles 

      Zúñiga Rojas, Ronald Alberto (2019-06)
      Considering a compact Riemann surface of genus greater or equal than two, a Higgs bundle is a pair composed of a holomorphic bundle over the Riemann surface, joint with an auxiliar vector field, so-called Higgs field. This ...
    • Geometric goodness of fit measure to detect patterns in data point clouds 

      Hernández Alvarado, Alberto José; Solís Chacón, Maikol; Zúñiga Rojas, Ronald Alberto (2019)
      The curse of dimensionality is a commonly encountered problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of ...
    • Geometrical correlation indices using homological constructions on manifolds 

      Solís Chacón, Maikol; Hernández Alvarado, Alberto José; Zúñiga Rojas, Ronald Alberto (2018)
      Abstract The course of dimensionality is a common problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of problems. ...
    • Stratifications on the Moduli Space of Higgs Bundles 

      Zúñiga Rojas, Ronald Alberto; Beier Gothen, Peter (2016-11-02)
      The moduli space of Higgs bundles has two stratifications. The Bia lynickiBirula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises ...
    • Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs 

      Beier Gothen, Peter; Zúñiga Rojas, Ronald Alberto (2020)
      We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural C ∗ -action on the moduli space. For general rank we provide ...
    • Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples 

      Zúñiga Rojas, Ronald Alberto (2020)
      There is an isomorphism between the moduli spaces of σ-stable holomorphic triples and some of the critical submanifolds of the moduli space of k-Higgs bundles of rank three, whose elements (E, ϕk ) correspond to variations ...