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Comparing compactifications of the moduli space of plane curves

Algebraic Geometry

Speaker: Kristin DeVleming, UCSD
Related Webpage: http://www.math.ucsd.edu/~kdevleming/
Location: 2112 MSB
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.