arXiv subjects

Amanda Hernandez

Publications and source records attributed to Amanda Hernandez.

4 recordsLinked to original sources

arXiv2026

What are the odds that a conic bundle over a finite field is rational?

We study rationality of conic bundles over finite fields defined over the line. In particular, for a fixed number $n$ of degenerate fibers, what is the proportion of good conic bundles that are rational over a finite field of order $q$? The Galois action on their Picard groups factors through the Weyl group $W(D_n)$, reducing rationality to a condition on signed permutation types. Using work of Colliot-Th\'el\`ene and Yang together with Chebotarev density, we compute the asymptotic proportion of such conic bundles that are rational as $q$ goes to infinity.

math.AG↗

arXiv2026

Moduli of conic surfaces over the line

We study moduli spaces and monodromy groups for surfaces fibered in conics over the projective line, with a view toward explicit presentations and arithmetic applications.

math.AG↗

arXiv2023

On non-counital Frobenius algebras

A Frobenius algebra is a finite-dimensional algebra $A$ which comes equipped with a coassociative, counital comultiplication map $Δ$ that is an $A$-bimodule map. Here, we examine comultiplication maps for generalizations of Frobenius algebras: finite-dimensional self-injective (quasi-Frobenius) algebras. We show that large classes of such algebras, including finite-dimensional weak Hopf algebras, come equipped with a nonzero map $Δ$ as above that is not necessarily counital. We also conjecture that this comultiplicative structure holds for self-injective algebras in general.

math.QA↗

arXiv2020

Maximum Covering Subtrees for Phylogenetic Networks

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-binary phylogenetic networks. We show that finding a phylogenetic tree covering the maximum number of nodes in a phylogenetic network can be be computed in polynomial time via an encoding into a minimum-cost maximum flow problem.

q-bio.PE↗