Every variety is birational to a weakly normal hypersurface

Abstract: Classically, it is known that every variety is birational to a projective hypersurface. For curves and surfaces, this hypersurface can be taken to have at worst nodal and at worst ordinary singularities, respectively. We will prove that in arbitrary dimension, this hypersurface can be taken to be weakly normal, and for smooth projective varieties of dimension at most five, this hypersurface can be taken to have semi-log canonical singularities. These results are due to Roberts and Zaare-Nahandi and to Doherty in characteristic zero, respectively, and to Rankeya Datta and myself in positive characteristic. Attendees will be asked to do some concrete computations with polynomials.

commutative algebraalgebraic geometrynumber theory

Audience: learners

Experimental Talks in Algebraic Geometry

Series comments: Description: Exploring ways to virtually communicate math

The recent shift from in-person to online talks provides us with an opportunity to explore new and interesting ways to communicate and learn things related to algebraic geometry. The goal of this seminar is to provide a space for speakers and audience members to do this exploration.

Each speaker will be given 50 minutes to create and lead an environment where topics related to algebraic geometry can be communicated and learned. How the speaker uses their time and creates such an environment is entirely up to them. They may try mixing pre-recorded and live aspects of a talk, they might try leading group work, who knows, it is entirely up to the speaker. The only request made of speakers is that they think critically about new ways to best use their time to promote the communication and learning of math. After the 50 minutes, a short group discussion will be held discussing how this form of online math communication went, and how it might be built upon. Everyone participating is asked to keep in mind that this is a place for experimentation.

This event is being organized by Juliette Bruce in association with the Algebraic Geometry Syndicate (AGS) discord server. Updates about the talks will be posted both here and on the AGS discord server. If you would like to join the AGS discord server please email juliette.bruce 'at' math.wisc.edu.