Algebraic Geometry Seminar

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Hypersurfaces with large automorphism groups

Speaker: Louis Esser, Princeton

Location: Warren Weaver Hall 512

Date: Tuesday, September 17, 2024, 3:30 p.m.

Synopsis:

A smooth hypersurface of dimension n and degree d in complex projective space always has finite automorphism group when the degree d is at least 3, unless (n,d) = (1,3) or (2,4).  Moreover, for each fixed pair (n,d), there is a finite upper bound on the order |Aut(X)|.  This bound was only known explicitly for certain small values of n and d.  In this talk, I'll describe results (joint with Jennifer Li) that exactly determine the upper bound on |Aut(X)| for every pair (n,d) and show that the Fermat hypersurface always achieves the upper bound apart from a finite number of exceptional cases.