2019
DOI: 10.1007/s10711-019-00503-8
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Embedding non-projective Mori dream space

Abstract: This paper is devoted to extend some Hu-Keel results on Mori dream spaces (MDS) beyond the projective setup. Namely, Q-factorial algebraic varieties with finitely generated class group and Cox ring, here called weak Mori dream spaces (wMDS), are considered. Conditions guaranteeing the existence of a neat embedding of a (completion of a) wMDS into a complete toric variety are studied, showing that, on the one hand, those which are complete and admitting low Picard number are always projective, hence Mori dream … Show more

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Cited by 2 publications
(4 citation statements)
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References 25 publications
(85 reference statements)
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“…Then results by Batyrev and Cox [8] and Bunnet [15] cannot be applied to guarantee a good definition of a moduli space M Y ∨ . By the way, observe that the computation performed in Theorem 5.3 is consistent with the definition of m Y ∨ given in (46). In fact…”
Section: 4supporting
confidence: 72%
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“…Then results by Batyrev and Cox [8] and Bunnet [15] cannot be applied to guarantee a good definition of a moduli space M Y ∨ . By the way, observe that the computation performed in Theorem 5.3 is consistent with the definition of m Y ∨ given in (46). In fact…”
Section: 4supporting
confidence: 72%
“…actually Hu-Keel proved this fact when X is projective, but this hypothesis is unnecessary (see e.g. [46,Thm. 3.7] and references therein).…”
Section: Nef(imentioning
confidence: 99%
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