4 papers · 1 filter
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…
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…
Exceptional Fano varieties with small minimal log discrepancy
Louis Esser, Jihao Liu, Chengxi Wang
We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective sp…
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…