Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number and boundedness of log minimal models of general type   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.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga