Back to Algebraic Geometry Seminar: Fall 2022
Algebraic Geometry Seminar
Date: Tuesday, Nov 29, 2022
Time: 3:30PM - 4:30PM
Location: LCB 323
Emelie Arvidsson
University of Utah
Title |
Properties of log-canonical threefold singularities in positive characteristics |
Abstract |
In this talk I will study if some well—known properties of log canonical threefold singularities over the complex numbers hold true over perfect fields of positive characteristics? For surfaces of Fano type the Kawamata–Viehweg vanishing theorem, which in general famously fails in positive characteristic p, hold true if p>5. This has the consequence that threefold klt singularities are Cohen–Macaulay in this characteristic. With this positive result at hand it is natural to ask if Kollárs theorem, asserting that the depth of a log canonical three-dimensional singularity is three at any closed point which itself is not a log canonical center, also can be extended to positive (possibly large enough) characteristics? Another natural and related question is if minimal log canonical centers are normal in (possibly large enough) positive characteristics? In this talk we will answer these two questions. This includes joint work with Bernasconi–Patakfalvi and Posva. |
Algebraic Geometry