7 papers
Counting odd genus curves with a marked rational -torsion point
Elvira Lupoian, Lazar Radicevic
In this paper we count, ordered by naive height, the genus curves over the rationals which admit a monic Weierstrass model of odd degree and whose Jacobian has a marked rationa…
Reduction Types of Genus 2 Curves
Edwina Aylward, Lilybelle Cowland Kellock, Vladimir Dokchitser +1
Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tab…
Intersections of the Ekedahl-Oort and Newton Strata of
Steven R. Groen, Elvira Lupoian, Mychelle Parker
The moduli space of principally polarised abelian varieties of dimension , defined over an algebraically closed field of characteristic , is studied throug…
Modular Units on and Quotients of the Cuspidal Group
Elvira Lupoian
Modular units are functions on modular curves whose divisors are supported on the cusps. They form a free abelian group of rank at most one less than the number of cusps. In this p…
Ceresa Cycles of
Elvira Lupoian, James Rawson
The Ceresa cycle is an algebraic 1-cycle on the Jacobian of an algebraic curve. Although it is homologically trivial, Ceresa famously proved that for a very general complex curve o…
Three-Torsion Subgroups and Wild Conductor Exponents of Plane Quartics
Elvira Lupoian, James Rawson
In this paper we give an algorithm to find the 3-torsion subgroup of the Jacobian of a smooth plane quartic curve with a marked rational point. We describe torsion points in te…