Mathematics Colloquia and Seminars
Comparing compactifications of the moduli space of plane curvesAlgebraic Geometry
|Speaker:||Kristin DeVleming, UCSD|
|Start time:||Wed, Apr 17 2019, 1:10PM|
Algebraic geometry provides many tools to compactify the moduli space of smooth plane curves of a fixed degree, and these tools generally yield very different compactifications. However, these compact moduli spaces should be birational, so a natural question to ask is how to relate these different compactifications.
In this talk, we will regard a plane curve of degree d > 3 as a pair (P^2, C) and study the GIT, K-stability, and KSB compactifications of pairs (P^2, a C) for different weights a. We will show, for a sufficiently small, we recover the GIT moduli of plane curves, and as a increases, the associated K-moduli spaces of log Fano pairs provide a way to interpolate between the GIT moduli and the KSB moduli of stable pairs. This is joint work with K. Ascher and Y. Liu.