Compact moduli space of plane curves via K-stability

Algebraic and Tropical Geometry
Event time: 
Friday, September 14, 2018 - 3:00pm
DL 431
Yuchen Liu
Speaker affiliation: 
Yale University
Event description: 

We study the K-stability compactification of moduli of log Fano pairs (P^2, aC) where C is a smooth plane curve of degree at least 4. We show that when a is small, the K-moduli compactification is isomorphic to the GIT moduli space of plane curves. We establish a framework of wall-crossing behaviors of these K-moduli spaces as a increases. Specifically, we show that the first wall-crossing of these K-moduli spaces are weighted blow-ups. We describe all wall-crossings for degree 4,5 and 6. We also relate the final K-moduli spaces to Hacking's moduli spaces. This is joint work in progress with K. Ascher, K. DeVleming, and P. Gallardo.

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