7 papers · 1 filter
Characterizing Varieties Using Birational Transformations
Nathan Chen, Louis Esser, Andriy Regeta +2
Suppose is an irreducible complex variety. We show that when is ruled, the group of birational transformations , as a group, determines up to birational transfo…
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…
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…
Rational weighted projective hypersurfaces
Louis Esser
A very general hypersurface of dimension and degree in complex projective space is rational if , but is expected to be irrational for all . Hypersurf…
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…
The dual complex of a -variety
Louis Esser
We introduce a new invariant of -varieties, the dual complex, which roughly measures how divisors in the complement of the free locus intersect. We show that the top homology gr…