arXiv subjects

Yerko Torres-Nova

Publications and source records attributed to Yerko Torres-Nova.

3 recordsLinked to original sources

arXiv2026

On the geography of 3-folds via asymptotic behavior of invariants

We study the geography problem for 3-folds of general type through the asymptotic behavior of invariants of $n$-th root covers. We first prove, in arbitrary dimension and for non-singular branch loci, that the Chern numbers are asymptotic to $n$ times the corresponding logarithmic Chern numbers of the base pair. In dimension three, for simple normal crossing branch divisors, we construct cyclic partial resolutions using toric methods and prove that, for asymptotic arrangements, the invariants $c_1^3, c_1c_2$, and $c_3$ have the same asymptotic behavior. We also obtain explicit families of 3-folds with ample canonical divisors that exhibit controlled Chern slopes.

math.AG↗

arXiv2026

Reciprocity For Dedekind Sums via Conical Zeta Values

We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach generalizes an integral method and uses Fourier analysis to show that the reciprocity for polynomial-type functions admits a geometric interpretation in terms of conical zeta values.

math.NT↗

arXiv2020

Periods of generalized Fermat curves

Let $k,n \geq 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface $S$ that admits a subgroup of conformal automorphisms $H \leq \mbox{Aut}(S)$ isomorphic to $\mathbb{Z}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\hat{\mathbb{C}}$ and has $n+1$ branch points, each one of order $k$. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.

math.AG↗