6 citations · 9 across the 12 of their papers we have counts for
9 papers · 1 filter
Families of curves in Vinberg representations
Jef Laga, Beth Romano
Inspired by orbit parametrizations in arithmetic statistics, we explain how to construct families of curves associated to certain nilpotent elements in -gra…
Lower bounds on heights of odd degree points of hyperelliptic curves
Jef Laga, Jack A. Thorne
We develop a reduction theory for the representation of on pairs of symmetric matrices. We apply this theory to the pencils of quadrics arising from div…
Kummers, spinors, and heights
Jef Laga, Jack A. Thorne
Let be a polynomial of nonzero discriminant, and let denote the Jacobian of the odd hyperelliptic curve $C : y^2 = f(…
100% of odd hyperelliptic Jacobians have no rational points of small height
Jef Laga, Jack A. Thorne
We study the universal family of odd hyperelliptic curves of genus over . We relate the heights of -points of Jacobians of curves in this family…
A positive proportion of monic odd-degree hyperelliptic curves of genus have no unexpected quadratic points
Jef Laga, Ashvin A. Swaminathan
Let be the family of monic odd-degree hyperelliptic curves of genus over . Poonen and Stoll have shown that for every , a positive proport…
Rational torsion points on abelian surfaces with quaternionic multiplication
Jef Laga, Ciaran Schembri, Ari Shnidman +1
Let be an abelian surface over whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic cur…
Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
Jef Laga
A simply laced Dynkin diagram gives rise to a family of curves over and a coregular representation, using deformations of simple singularities and Vinberg theory respe…
Arithmetic statistics of Prym surfaces
Jef Laga
We consider a family of abelian surfaces over arising as Prym varieties of double covers of genus- curves by genus- curves. These abelian surfaces carry a polari…
The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3
Jef Laga
We show that the average size of the -Selmer group of the family of Jacobians of non-hyperelliptic genus- curves with a marked rational hyperflex point, when ordered by a nat…