Intersection theory on moduli of hyperplane arrangements and marked del Pezzo surfaces

Abstract: This talk is about the intersection theory of two of the first examples of compact moduli spaces of higher-dimensional varieties: the log canonical compactification of the moduli space of marked del Pezzo surfaces, and the stable pair compactification of the moduli space of hyperplane arrangements. The latter space is the natural higher-dimensional version of $\overline{M}_{0,n}$, the moduli space of n-pointed rational curves, but its geometry can in general be arbitrarily complicated. On the other hand, the former space, which can also be viewed as a higher-dimensional generalization of $\overline{M}_{0,n}$, by construction has nice geometry on the boundary, and this leads (conjecturally for degree 1,2) to a presentation of its Chow ring entirely analogous to Keel's famous presentation of the Chow ring of $\overline{M}_{0,n}$. I will describe work in progress using the relationships between these moduli spaces in order to describe the intersection theory of the moduli space of stable hyperplane arrangements.

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.