Toward the logarithmic Hilbert scheme

Abstract: Logarithmic geometry provides tools to work relative a normal crossings divisor, including normal crossings degenerations. I will report on work in progress with Mattia Talpo and Richard Thomas to define a natural logarithmic analogue of the ordinary Hilbert scheme. Immediate applications include induced good degenerations of Hilbert schemes of points. Our point of view also suggests a definition of tropical Hilbert schemes. One larger aim is to develop robust logarithmic methods to deal with coherent sheaves in maximal degenerations as they appear in mirror symmetry.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html