Wall crossing for K-moduli spaces of plane curves

Abstract: This talk will focus on compactifications of the moduli space of smooth plane curves of degree d at least 4. We will regard a plane curve as a log Fano pair (P2, aC), where a is a rational number, and study the compactifications arising from K stability for these pairs and log Fano pairs in general. We establish a wall crossing framework to study these spaces as a varies and show that, when a is small, the moduli space coming from K stability is isomorphic to the GIT moduli space. We describe all wall crossings for degree 4, 5, and 6 plane curves and discuss the picture for general Q-Gorenstein smoothable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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