Louis Esser

collaborators

5 papers

math.AG2025

Characterizing Varieties Using Birational Transformations

Nathan Chen, Louis Esser, Andriy Regeta +2

Suppose $X$ is an irreducible complex variety. We show that when $X$ is ruled, the group of birational transformations $B i r (X)$ , as a group, determines $X$ up to birational transfo…

math.AG2025

Weighted surfaces with maximal Picard number

Louis Esser, Jennifer Li

An algorithm due to Shioda computes the Picard number for certain surfaces which are defined by a single equation with exactly four monomials, called Delsarte surfaces. We consider…

math.AG2024

Hypersurfaces with large automorphism groups

Louis Esser, Jennifer Li

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hyper…

math.AG2024

Rational weighted projective hypersurfaces

Louis Esser

A very general hypersurface of dimension $n$ and degree $d$ in complex projective space is rational if $d \leq 2$ , but is expected to be irrational for all $n, d \geq 3$ . Hypersurf…

math.AG2024

Group actions and irrationality in surface families

Nathan Chen, Louis Esser

Rationality specializes in families of surfaces, even with mild singularities. In this paper, we study the analogous question for the degree of irrationality. We prove a specializa…