Singularities of generic projection hypersurfaces

Algebra and Number Theory Seminar

Meeting Details

For more information about this meeting, contact Allyson Borger, Kirsten Eisentraeger, Jack Huizenga, Mihran Papikian, Ae Ja Yee, John Lesieutre.

Speaker: Takumi Murayama, Princeton

Abstract: Classically, it is known that every finitely generated field over an algebraically closed field is the function field of a hypersurface in some projective space. Using generic linear projections, one can show that this hypersurface can be taken to have at worst nodal singularities in dimension one, or at worst ordinary singularities in dimension two. We present a generalization of these results to dimensions up to five, in which case the relevant class of singularities is that which appears on degenerations of smooth varieties in moduli theory. This result is due to Doherty over the complex numbers, and is joint with Rankeya Datta in positive characteristic.

Room Reservation Information

Room Number: 106 McAllister

Date: 12/12/2019

Time: 11:00am - 11:50am