Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log Sarkisov Program   The purpose of this paper is two-fold. The first is to give a tutorial
introduction to the Sarkisov program, a 3-dimensional generalization of
Castelnuovo-N\"other Theorem ``untwisting" birational maps between Mori fiber
spaces, which was recently established by Corti after Sarkisov and Reid.
  The second is an attempt to give a logarithmic generalization of the program,
introducing the notion of the Sarkisov relation. We give a simple description
of the structure of the program and clarify the mechanism of termination
connected to the boundedness conjecture of (log) Q-Fano n-folds by Borisov.

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The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex