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

Diletta Martinelli; Stefan Schreieder; Luca Tasin

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arXiv · 1610.08932

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

Diletta Martinelli·Stefan Schreieder·Luca Tasin

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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 $K_X+D$ 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 $K_X+D$. We further show that all n-dimensional projective klt pairs (X,D), such that $K_X+D$ 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.

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Diletta Martinelli, Stefan Schreieder, Luca Tasin. 2016-10-27. On the number and boundedness of log minimal models of general type. https://arxiv.org/abs/1610.08932

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