arXiv subjects

Anibal Aravena

Publications and source records attributed to Anibal Aravena.

3 recordsLinked to original sources

arXiv2026

Pseudo-hyperbolicity of Horikawa surfaces

Horikawa surfaces are minimal complex algebraic surfaces of general type with minimal Chern slope, satisfying either $c_2=5c^2_1+36$ if $c_1^2$ is even, or $c_2=5c^2_1+30$ if $c_1^2$ is odd. We prove that very general Horikawa surfaces with $p_g\ge 5$ contain only finitely many rational or elliptic curves. Moreover, we provide an explicit characterization and count of these curves. Our results also apply to very general Horikawa surfaces of the first kind with $p_g\in \{3,4\}.$

math.AG↗

arXiv2025

Fano visitor problem for K3 surfaces

Let $X$ be a K3 surface with Picard number 1 and genus $g$, such that $g\not\equiv 3 \mod 4$. In this paper, we show that $X$ is a Fano visitor, i.e., there is a smooth Fano variety $Y$ and an embedding $D^b(X)\hookrightarrow D^b(Y)$ given by a fully faithful functor. If $g\equiv 3\mod 4$, we construct a smooth weak Fano variety $Y$. Our proof is based on several results concerning a sequence of flips associated with a K3 surface and an ample line bundle. This sequence is constructed by using the work of Bayer and Macrì on the description of the birational geometry of a moduli space of sheaves on a K3 surface through Bridgeland stability conditions, and the study of the fixed locus of antisymplectic involutions on hyperkähler manifolds by Saccà, Macrì, O'Grady, and Flapan.

math.AG↗

arXiv2020

Iterated constructions of completely normal polynomials

The $R_{σ,t}$-transform introduced by Bassa and Menares can be used to construct families of irreducible polynomials in $\mathbb{F}_q[x]$. This iterative construction is a generalization of Cohen's $R$-transform. For this transform, Chapman proved that under some conditions, the polynomials in the resulting family are completely normal. In this paper we establish conditions ensuring that the polynomials obtained by using the $R_{σ,t}$-transform are completely normal polynomials and we give a simple proof of Chapman's result.

math.RA↗