On finiteness of log canonical models

Abstract

Let $(X,\Delta )/U$ be klt pairs and $Q$ be a convex set of divisors. Assuming that the relative Kodaira dimensions are non-negative, then there are only finitely many log canonical models when the boundary divisors varying in a relatively compact rational polytope in $Q$. As a consequence, we show the existence of the log canonical model for a klt pair $(X,\Delta )/U$ with real coefficients.

23 pages

References in corpus (1)

• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring

Cited by in corpus (1)

• A variant of the effective adjunction conjecture with applications