Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, Feb 7, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
@ 4:30pm, Virtual
Takumi Murayama
Purdue University
Title |
Pure subrings of Du Bois singularities are Du Bois singularities Note the unusual time! |
Abstract |
Let (R \rightarrow S) be a pure map of rings. If (S) is regular, then it is known that (R) has rational singularities, and hence is Cohen-Macaulay. This result applies in particular to inclusions of rings of invariants by linearly reductive groups, split maps, and faithfully flat maps. In this talk, I will discuss my recent work (joint with Charles Godfrey) showing that if (R) and (S) are essentially of finite type over the complex numbers, and (S) has Du Bois singularities, then (R) has Du Bois singularities. Our result is new even when (R \rightarrow S) is faithfully flat. As a consequence, under the same hypotheses on (R \rightarrow S), if (S) has log canonical type singularities and the canonical divisor on (R) is Cartier, then (R) has log canonical singularities. |
Algebraic Geometry