Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, Mar 21, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Christopher Chiu
TU Eindhoven
Title |
Isosingularity of algebraic varieties |
Abstract |
In this talk we will consider the formal-local singularity type of points on an algebraic variety X. Extending work of Ephraim and Hauser-Mueller, we show that the subset of points with a fixed singularity type is locally closed in the Zariski topology; and the associated reduced subscheme, called isosingular locus, is smooth. Moreover, over a field of characteristic 0, we prove the existence of a decomposition of the formal neighborhood at each point. In positive characteristics we give counterexamples and relate them to questions on finite determinacy. Finally, we discuss connections to the local geometry of arc spaces and in particular the Drinfeld-Grinberg-Kazhdan theorem. This talk covers joint work with Herwig Hauser. |
Algebraic Geometry