Weighted surfaces with maximal Picard number

Pretalk title: An introduction to weighted projective spaces

Abstract: The focus of today's main talk involves certain surfaces in weighted projective space. This space is defined similarly to the usual projective space, except now we may attach nontrivial weights to the coordinates. In this pretalk, I will introduce weighted projective spaces, explain some of its interesting properties, and provide many examples.

 

Talk title: Weighted surfaces with maximal Picard number

Abstract: 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 this method for surfaces in weighted projective 3-space with quotient singularities. In this talk, I will explain a criterion for such a weighted Delsarte surface X to have maximal Picard number. This condition is surprisingly related to the automorphism group of X. This is joint work with Louis Esser.