arXiv subjects

Jorge Olivares

Publications and source records attributed to Jorge Olivares.

5 recordsLinked to original sources

arXiv2026

Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces

We study holomorphic foliations on projective spaces that leave smooth projective complete intersection surfaces $M$ invariant. We determine precisely for which degrees such foliations on $M$ exist. As a consequence, we obtain new bounds for the classical Poincaré problem for smooth projective complete intersection surfaces and prove that previously known bounds for smooth hypersurfaces in $\mathbb{P}^3$ are optimal. Furthermore, for a foliation $[s]$ on $M$ with isolated singularities and for degrees beyond an explicit bound that we provide, we show that a section $s'$ has singular scheme containing that of $s$ if and only if $s'=ϕ(s)$ for some global endomorphism $ϕ$ of the tangent bundle of $M$.

math.AG↗

arXiv2025

Accurate analytic approximation for a fractional differential equation with a modified Bessel function term

A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact analytical solution of this equation is expressed as the product of two modified Bessel functions. The approximation is constructed using an extended multipoint quasi-rational method, which simultaneously incorporates the series expansion and the asymptotic behavior of the Bessel function. A key modification is introduced in the structure of the fitting function, allowing it to reproduce two terms of the asymptotic expansion instead of only one, thereby improving accuracy for large arguments. Numerical analysis shows that for representative parameter values, the maximum relative error between the proposed fitting function and the exact solution of the fractional differential equation is approximately $0.18\%$, demonstrating the high precision achieved with only six fitting parameters.

math.GM↗

arXiv2025

Foliations on Projective Complete Intersection K3 Surfaces

We study foliations $\mathscr{F}$ on projective complete intersection K3 surfaces $X \hookrightarrow \mathbb{P}^n$, where $\mathscr{F}$ has isolated singularities and it is the restriction of a foliation of degree $d$ on $\mathbb{P}^n$ that leaves $X$ invariant. We compute the values of the degrees $d$ for which $\mathscr{F}$ is uniquely determined by its singular scheme.

math.AG↗

arXiv2021

Visualizing superconductivity in an inversion-symmetry-broken doped Weyl semimetal

The Weyl semimetal MoTe$_2$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5K, but suppress the Td structure phase that is essential for the emergence of Weyl state. A microscopic understanding of possible coexistence of enhanced superconductivity and the Td phase has not been established so far. Here, we use scanning tunneling microscopy (STM) to study a optimally doped new superconductor MoTe$_{1.85}$Se$_{0.15}$ with bulk Tc ~ 1.5K. By means of quasiparticle interference imaging, we identify the existence of low temperature Td phase with broken inversion symmetry where superconductivity globally coexists. Consistently, we find that the superconducting coherence length, extracted from both the upper critical field and the decay of density of states near a vortex, is much larger than the characteristic length scale of existing dopant derived chemical disorder. Our findings of robust superconductivity arising from a Weyl semimetal normal phase in MoTe$_{1.85}$Se$_{0.15}$, makes it a promising candidate for realizing topological superconductivity.

cond-mat.supr-con↗

arXiv2020

Foliations with isolated singularities on Hirzebruch surfaces

We study foliations $\mathcal{F}$ on Hirzebruch surfaces $S_δ$ and prove that, similarly to those on the projective plane, any $\mathcal{F}$ can be represented by a bi-homogeneous polynomial affine $1$-form. In case $\mathcal{F}$ has isolated singularities, we show that, for $ δ=1 $, the singular scheme of $\mathcal{F}$ does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For $δ\neq 1$, we prove that the singular scheme of $\mathcal{F}$ does not determine the foliation. However we prove that, in most cases, two foliations $\mathcal{F}$ and $\mathcal{F}'$ given by sections $s$ and $s'$ have the same singular scheme if and only if $s'=Φ(s)$, for some global endomorphism $Φ$ of the tangent bundle of $S_δ$.

math.AG↗