M ¯ 0 , n is not a Mori dream space

Ana-Maria Castravet; Jenia Tevelev

doi:10.1215/00127094-3119846

Abstract

Building on the work of Goto, Nishida, and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with $n$ punctures is not a Mori dream space for $n\gt 133$ . This answers a question posed by Hu and Keel.

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Ana-Maria Castravet. Jenia Tevelev. " $\overline {M}_{0,n}$ is not a Mori dream space." Duke Math. J. 164 (8) 1641 - 1667, 1 June 2015. https://doi.org/10.1215/00127094-3119846

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Received: 15 December 2013; Revised: 25 August 2014; Published: 1 June 2015

First available in Project Euclid: 28 May 2015

zbMATH: 1343.14013

MathSciNet: MR3352043

Digital Object Identifier: 10.1215/00127094-3119846

Subjects:

Primary: 14E30 , 14H10

Secondary: 14J60 , 14M25 , 14N20

Keywords: elementary transformations , moduli of rational curves , Mori dream spaces , symbolic Rees algebras , toric varieties , weighted projective planes

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