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arxiv: 1407.6344 · v1 · pith:FY47Z3EDnew · submitted 2014-07-23 · 🧮 math.AG · math.AC

Some non-finitely generated Cox rings

Jos\'e Luis Gonz\'alez , Kalle Karu This is my paper
classification 🧮 math.AG math.AC
keywords generatedfinitelyringsblowncastravetcurvesfamilygenus
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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 of stable n-pointed genus zero curves does not have a finitely generated Cox ring if n is at least 13.

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  1. The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$

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    The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.