2019
DOI: 10.1016/j.jpaa.2019.01.014
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Mori Dream Spaces and blow-ups of weighted projective spaces

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Cited by 7 publications
(4 citation statements)
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“…In this last section we apply our results to the blowing-up of a toric fiber space along a section, with the purpose of producing new examples of varieties with nonfinitely generated Cox ring (see e.g. [7,8,13,16]). Construction 6.1.…”
Section: Blowing-ups Of Toric Fiber Spacesmentioning
confidence: 99%
See 1 more Smart Citation
“…In this last section we apply our results to the blowing-up of a toric fiber space along a section, with the purpose of producing new examples of varieties with nonfinitely generated Cox ring (see e.g. [7,8,13,16]). Construction 6.1.…”
Section: Blowing-ups Of Toric Fiber Spacesmentioning
confidence: 99%
“…Example 6.4. Let P(a) be a weighted projective space whose blowing-up at a general point has non-finitely generated Cox ring (see for instance [7,8,13,16]), and let Σ 0 ⊆ (N 0 ) Q be a defining fan for P(a). Let N := N 0 ⊕ Z.…”
Section: Blowing-ups Of Toric Fiber Spacesmentioning
confidence: 99%
“…The study of toric varieties whose blowup at a general point is not a Mori dream space has attracted a lot of interest recently (see [GK16], [HKL18], [GK19], [He19], [KN19], [GAGK20]) and often plays a pivotal role in determining whether a given variety is a Mori dream space (e.g. [CT15], [GK16], [HKL18]).…”
Section: Introductionmentioning
confidence: 99%
“…We state a conjecture which generalizes a theorem of González and Karu [GK16]. Chapter 5 is based on the paper [He19b], where we describe a sufficient condition in higher dimensions for the blow-up of a weighted projective space P(a, b, c, d 1 , • • • , d n−2 ) at the identity point not to be a Mori Dream Space. We constructed several infinite sequences of weights satisfying this condition in all dimensions n ≥ 3, some of which generalizing the results in [GNW94].…”
Section: Chapter 1 Introduction 11 a Brief Overviewmentioning
confidence: 95%