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arXiv · 2412.15723

K-moduli with real coefficients

Yuchen Liu·Chuyu Zhou
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Abstract

In this paper, we develop an algebraic K-stability theory (e.g. special test configuration theory and optimal destabilization theory) for log Fano $\mathbb R$-pairs, and construct a proper K-moduli space to parametrize K-polystable log Fano $\mathbb R$-pairs with some fixed invariants (e.g. dimension, volume, coefficients). All of these are well-known for log Fano $\mathbb Q$-pairs, and the strategy in this paper is trying to reduce the problems (in many cases) to $\mathbb Q$-coefficients case rather than rebuilding the whole program as in $\mathbb Q$-coefficients case.

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Yuchen Liu, Chuyu Zhou. 2024-12-20. K-moduli with real coefficients. https://arxiv.org/abs/2412.15723

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