2019
DOI: 10.1080/10586458.2018.1547232
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Blow-Ups of Toric Surfaces and the Mori Dream Space Property

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Cited by 3 publications
(4 citation statements)
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“…For m = 1 there is a unique curve defined by f (x, y) = 1 − y. This curve with m = 1 appeared in all examples of [8][9][10][11]. Similarly, for m = 2 there is a unique curve defined by f (x, y) = 3 − x − y − x −1 y −1 .…”
Section: Introductionmentioning
confidence: 89%
See 1 more Smart Citation
“…For m = 1 there is a unique curve defined by f (x, y) = 1 − y. This curve with m = 1 appeared in all examples of [8][9][10][11]. Similarly, for m = 2 there is a unique curve defined by f (x, y) = 3 − x − y − x −1 y −1 .…”
Section: Introductionmentioning
confidence: 89%
“…For small values of M and N , the possibly degenerate triangles IT (0, 1), IT (1, 0), RT (1, 0), RT (1, 1) support the same negative curve with vanishing order m = 1. This case has been widely studied in the literature [8][9][10][11]14]. The present paper does not say anything more about the m = 1 case.…”
Section: Introductionmentioning
confidence: 89%
“…Then w ≤ 1/2. By Theorem 2.6 of [He19a] (Theorem 4.2.6), if w ≤ 1/2, then Bl p P(a, b, c) is a MDS, which contradicts the assumption. Therefore g 2 = 1, and…”
Section: Comparison With González and Karu's Examplesmentioning
confidence: 94%
“…We study whether such blow-ups are Mori Dream Spaces. Chapter 4 is based on the paper [He19a], where we gave new criterion for some toric surfaces of Picard number one. We state a conjecture which generalizes a theorem of González and Karu [GK16].…”
Section: Chapter 1 Introduction 11 a Brief Overviewmentioning
confidence: 99%