Advanced Studies in Pure Mathematics

Finite generation and geography of models

Anne-Sophie Kaloghiros, Alex Küronya, and Vladimir Lazić

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There are two main examples where a version of the Minimal Model Program can, at least conjecturally, be performed successfully: the first is the classical MMP associated to the canonical divisor, and the other is Mori Dream Spaces. In this paper we formulate a framework which generalises both of these examples. Starting from divisorial rings which are finitely generated, we determine precisely when we can run the MMP, and we show why finite generation alone is not sufficient to make the MMP work.

Article information

Minimal Models and Extremal Rays (Kyoto, 2011), J. Kollár, O. Fujino, S. Mukai and N. Nakayama, eds. (Tokyo: Mathematical Society of Japan, 2016), 215-245

Received: 6 February 2012
Revised: 6 August 2012
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538622707

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E30: Minimal model program (Mori theory, extremal rays)


Kaloghiros, Anne-Sophie; Küronya, Alex; Lazić, Vladimir. Finite generation and geography of models. Minimal Models and Extremal Rays (Kyoto, 2011), 215--245, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07010215.

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