Duke Mathematical Journal

New outlook on the Minimal Model Program, I

Paolo Cascini and Vladimir Lazić

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We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.

Article information

Duke Math. J., Volume 161, Number 12 (2012), 2415-2467.

First available in Project Euclid: 6 September 2012

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Zentralblatt MATH identifier

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14E99: None of the above, but in this section


Cascini, Paolo; Lazić, Vladimir. New outlook on the Minimal Model Program, I. Duke Math. J. 161 (2012), no. 12, 2415--2467. doi:10.1215/00127094-1723755. https://projecteuclid.org/euclid.dmj/1346936110

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