Nelson Alvarado

activity

20222026

collaborators

5 papers

math.AG2026

Seshadri constants and hyperelliptic curves on abelian varieties

Nelson Alvarado

Given a principally polarized abelian variety, we give a sufficient condition for the van Geemen-van der Geer locus $Γ_{00}$ to be positive dimensional. Along the way, we prove a s…

math.AG2025

Abelian varieties analogs of two results about algebraic curves

Nelson Alvarado, Giuseppe Pareschi

We characterize decomposable principally polarized abelian varieties of the form $E \times B$ , with $E$ an elliptic curve, in two different ways, which are, surprisingly, completely…

math.AG2024

Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties

Nelson Alvarado

Given a closed subscheme $Z$ of a polarized abelian variety $(A, ℓ)$ we define its vanishing threshold with respect to $ℓ$ and relate it to the Seshadri constant of the ideal…

math.AG2024

Semihomogenous vector bundles, $Q$ -twisted sheaves, duality, and linear systems on abelian varieties

Nelson Alvarado, Giuseppe Pareschi

In this paper we point out the natural relation between $Q$ -twisted objects of the derived category of abelian varieties, cohomological rank functions, and semihomogeneous…

math.AG2022

Degenerations of non-simple abelian surfaces

Nelson Alvarado

We study degenerations of non-simple principally polarized abelian surfaces to the boundary in the toroidal compactification of $A_{2}$ , and describe the degenerate abelian…

Seshadri constants and hyperelliptic curves on abelian varieties

Abelian varieties analogs of two results about algebraic curves

Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties

Semihomogenous vector bundles, Q-twisted sheaves, duality, and linear systems on abelian varieties

Degenerations of non-simple abelian surfaces

Semihomogenous vector bundles, $Q$ -twisted sheaves, duality, and linear systems on abelian varieties