6 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(…
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…
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…
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…