K-moduli with real coefficients

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.

50 pages, comments welcome