Algebraic Geometry Seminar
Janet Page
University of Michigan
Extremal Hypersurfaces in Positive Characteristic
Abstract: What is the most singular possible (reduced) hypersurface in positive characteristic? One answer to this question comes from finding a lower bound on an invariant called the F-pure threshold of a polynomial in terms of its degree. In this talk, I'll introduce a new class of hypersurfaces which obtain a minimal F-pure threshold and discuss some of their surprising algebraic and geometric properties. They are cut out by polynomials that we call Frobenius forms, which have a rich algebraic structure coming from the fact that they have a matrix factorization mirroring the theory of quadratic forms. In the surface case, we'll see that they share some geometric properties with cubic surfaces. This is based on joint work with Zhibek Kadyrsizova, Jennifer Kenkel, Jyoti Singh, Karen E Smith, Adela Vraciu, and Emily E Witt, as well as more recent joint work with Anna Brosowsky, Tim Ryan, and Karen Smith.
Monday October 4, 2021 at 3:00 PM in Zoom