Back to Algebraic Geometry Seminar: Fall 2023
Algebraic Geometry Seminar
Date: Tuesday, Oct 31, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Sridhar Venkatesh
University of Michigan
Title |
Higher Du Bois and Higher Rational Singularities |
Abstract |
k-Du Bois and k-rational singularities are recently introduced refinements of the classical notions of Du Bois and rational singularities, and they have been extensively studied in the local complete intersection (lci) case. Building on a well known result of Kovács that rational singularities are Du Bois, we prove that k-rational singularities are k-Du Bois. This extends previous work of Mustaţă-Popa and Friedman-Laza in the lci and the isolated singularities cases. Additionally, since Kähler differentials are typically not reflexive outside the lci case, we propose new definitions of these singularities that depend only on the cohomologies of the Du Bois complex and not on the behaviour of Kähler differentials. This is based on joint work with Wanchun Shen and Anh Duc Vo. |
Algebraic Geometry