$F$-singularities and singularities in birational geometry - Part 1

Abstract: $F$-singularities are singularities in positive characteristic defined using the Frobenius map and there are four basic classes of $F$-singularities: $F$-regular, $F$-pure, $F$-rational and $F$-injective singularities. They conjecturally correspond via reduction modulo $p$ to singularities appearing in complex birational geometry. In the first talk, I will survey basic properties of $F$-singularities. In the second talk, I will explain what is known and what is not known about the correspondence of $F$-singularities and singularities in birational geometry. If the time permits, I will also discuss its geometric applications.

commutative algebra

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home