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K-moduli of Fano threefolds and genus four curves

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EMGW04 - K-stability and moment maps

In this talk, I will show that the K-moduli space of Fano threefolds obtained by blowing up P3 along (2, 3)-complete intersection curves is isomorphic to a VGIT moduli space studied by Casalaina-Martin-Jensen-Laza. In particular, it is a two-step birational modification of the GIT moduli space of (3, 3)-curves on P1×P^1. Our strategy is the moduli continuity method with moduli of lattice-polarized K3 surfaces, general elephants and Sarkisov links as new ingredients. Based on joint work with Junyan Zhao.

This talk is part of the Isaac Newton Institute Seminar Series series.

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