Geodesic
Examples of Non-finitely Generated Cox Rings
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 267-285

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We bring examples of toric varieties blown up at a point in the torus that do not have finitely generated Cox rings. These examples are generalizations of our earlier work, where toric surfaces of Picard number 1 were studied. In this article we consider toric varieties of higher Picard number and higher dimension. In particular, we bring examples of weighted projective 3-spaces blown up at a point that do not have finitely generated Cox rings.
DOI : 10.4153/CMB-2018-029-6
Mots-clés : Cox ring, Mori dream space, toric variety 
González, José Luis; Karu, Kalle. Examples of Non-finitely Generated Cox Rings. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 267-285. doi: 10.4153/CMB-2018-029-6
@article{10_4153_CMB_2018_029_6,
     author = {Gonz\'alez, Jos\'e Luis and Karu, Kalle},
     title = {Examples of {Non-finitely} {Generated} {Cox} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {267--285},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-029-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-029-6/}
}
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