Deformations of Smooth Projective Toric Varieties

Abstract: We can study how a given scheme X fits into a family using the tools from the deformation theory. One begins by using infinitesimal methods, studying possible obstructions, and attempting to construct a family called a versal deformation, which collects all possible deformations. If X is a smooth projective toric variety, combinatorial descriptions of the space of first-order deformations and the obstruction to second-order deformation given by the cup product have been studied. In this talk, I will present these descriptions with an example of a smooth projective toric threefold with a quadratic obstruction. In addition, I will discuss my current research, which provides a combinatorial iterative procedure for finding higher-order obstructions.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca