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Some non-finitely generated Cox rings
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 5 / May 2016
- Published online by Cambridge University Press:
- 22 December 2015, pp. 984-996
- Print publication:
- May 2016
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- Article
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We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space
$\overline{M}_{0,n}$ of stable 
$n$-pointed genus-zero curves does not have a finitely generated Cox ring if 
$n$ is at least 
$13$.
