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 nonnegative, 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.01370
 arXiv:
 arXiv:2006.01370
 Bibcode:
 2020arXiv200601370L
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 23 pages