arXiv subjects

Diego Yépez

Publications and source records attributed to Diego Yépez.

4 recordsLinked to original sources

arXiv2026

An algorithmic reduction to canonical forms for vector bundles on anisotropic conics

We describe a polynomial complexity algorithm for reducing transition matrices, for vector bundles glued along a clutching-type cover of a real anisotropic conic, to canonical block diagonal forms. This is a generalization, to the real anisotropic form, of the classification of vector bundles on the Riemann sphere by their canonical diagonal forms due to Grothendieck and Birkhoff. To enable our algorithm, we provide an elementary algebraic proof for the result, due to Biswas-Nagaraj and Novakovic, of the decomposition of vector bundles on real anisotropic conics into sums of indecomposable vector bundles of rank at most 2. While our algorithm and our proof of this decomposition focus solely on the setting of a real anisotropic conic, our methods are immediately generalizable to anisotropic conics over arbitrary fields.

math.AG↗

arXiv2025

Monodromy Representations: Decomposing Rank-Three Bundles over the Projective Line with Three Marked Points

Given a monodromy representation $ρ$ of the projective line minus $m$ points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition; i.e., computing the roots. Particularly, we use the monodromy derivative to compute the roots for all three-dimensional $ρ$ when $m = 3$.

math.AG↗

arXiv2025

Stationary solutions with vacuum for a hyperbolic-parabolic chemotaxis model in dimension two

In this research, we study the existence of stationary solutions with vacuum to a hyperbolic-parabolic chemotaxis model with nonlinear pressure in dimension two that describes vasculogenesis. We seek solutions in the radial symmetric class of the whole space, in which the system will be reduced to a system of ODE's on $(0,\infty)$. The fundamental solutions to the ODE system are the Bessel functions of different types. We find two nontrivial solutions. One is formed by half bump (positive density region) starting at $r=0$ and a region of vacuum on the right. Another one is a full nonsymmetric bump away from $r=0$. These solutions bear certain resemblance to in vitro vascular network and the numerically produced structure by Gamba et al arXiv:cond-mat/0303468v1. We also show the nonexistence of full bump starting at $r=0$ and nonexistence of full symmetric bump away from $r=0$.

math.AP↗

arXiv2025

Computing the Roots of Twisting Sheaves over the Projective Line arising from Monodromy Representations

Given a monodromy representation $ρ$ of the projective line minus $m$ points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition; i.e. computing the roots. Particularly, we compute the roots for all finite-dimensional $ρ$ when $m = 2$ and for all $ρ$ of dimension less than $3$ when $m = 3$.

math.AG↗