Moduli of hypersurfaces in weighted projective space
Starts 24 Jan 2019 14:30
Ends 24 Jan 2019 15:30
Central European Time
Leonardo Building - Luigi Stasi Seminar Room
Abstract: The moduli space of smooth hypersurfaces in projective space was constructed by Mumford in the 60’s using his newly developed classical (a.k.a. reductive) Geometric Invariant Theory. I wish to generalise this construction to hypersurfaces in weighted projective space (or more generally orbifold toric varieties). The automorphism group of a toric variety is in general non-reductive and I will use new results in non-reductive GIT, developed by F. Kirwan et al., to construct a moduli space of quasismooth hypersurfaces. I will give geometric characterisations of notions of stability arising from non-reductive GIT.