Douglas Ulmer

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20012026

most citedGeometric non-vanishing

15 citations · 57 across the 25 of their papers we have counts for

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math.AG2025

New unlikely intersections on elliptic surfaces

Douglas Ulmer, José Felipe Voloch

Consider a Jacobian elliptic surface $E \to C$ with a section $P$ of infinite order. Previous work of the first author and Urzúa over the complex numbers gives a bound on the numbe…

math.AG2020

Bounding tangencies of sections on elliptic surfaces

Douglas Ulmer, Giancarlo Urzúa

Given an elliptic surface $E \to C$ over a field $k$ of characteristic zero equipped with zero section $O$ and another section $P$ of infinite order, we give a si…

math.AG2019

Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces

Douglas Ulmer, Giancarlo Urzúa

We consider elliptic surfaces $E$ over a field $k$ equipped with zero section $O$ and another section $P$ of infinite order. If $k$ has characteristic zero, we show there…

math.AG2014

Low-dimensional factors of superelliptic Jacobians

Thomas Occhipinti, Douglas Ulmer

Given a polynomial $f \in C [x]$ , we consider the family of superelliptic curves $y^{d} = f (x)$ and their Jacobians $J_{d}$ for varying integers $d$ . We show that for any integer $…

math.AG2014

Rational curves on elliptic surfaces

Douglas Ulmer

We prove that a very general elliptic surface $E \to P^{1}$ over the complex numbers with a section and with geometric genus $p_{g} \geq 2$ contains no rational curves ot…