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Title:
On K-stability and K-moduli of Fano hypersurfaces
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Abstract:
It is accepted knowledge that K-stability provides the right framework for the compact moduli of Fano varieties. While it is conjectured that all smooth Fano hypersurfaces are K-polystable, very little is known about expectations on the structure of their K-moduli except in low degrees. I will survey known results on both K-stability of hypersurfaces and their moduli, with a focus on recent progress on quartic 3-folds in joint work with Cheltsov, Kasprzyk, Liu, and Petracci.
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