On the number and boundedness of log minimal models of general type

Diletta Martinelli, Stefan Schreieder, Luca Tasin

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the number of marked minimal models of an n-dimensional smooth complex projective variety of general type can be bounded in terms of its volume, and, if n=3, also in terms of its Betti numbers. For an n-dimensional projective klt pair (X,D) with Kx + D big, we show more generally that the number of its weak log canonical models can be bounded in terms of the coefficients of D and the volume of . We further show that all n-dimensional projective klt pairs (X,D), such that Kx + D is big and nef of fixed volume and such that the coefficients of D are contained in a given DCC set, form a bounded family. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family.
Original languageEnglish
Number of pages27
JournalAnnales Scientifiques de l'École Normale Supérieure
Publication statusAccepted/In press - 11 Oct 2018

Fingerprint Dive into the research topics of 'On the number and boundedness of log minimal models of general type'. Together they form a unique fingerprint.

Cite this