P. Engel

activity

20182022

collaborators

3 papers

math.AG2022

The Manin-Mumford conjecture in genus 2 and rational curves on K3 surfaces

Philip Engel, Raju Krishnamoorthy, Daniel Litt

Let $A$ be a simple abelian surface over an algebraically closed field $k$ . Let $S \subset A (k)$ be the set of torsion points $x$ of $A$ such that there exists a genus $2$ curve $C$ …

math.AG2021

The flex divisor of a K3 surface

Valery Alexeev, Philip Engel

The flex divisor of a primitively polarized K3 surface $(X, L)$ of degree $L^{2} = 2 d$ is, generically, the locus of all points $x \in X$ for which there exists a pencil $V \subset ∣ L ∣$ w…

math.AG2018

Hurwitz Theory of Elliptic Orbifolds, II

Philip Engel

An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an el…