Examples of Mori dream surfaces of general type with p = 0

Keum, JongHae; Lee, Kyoung-Seog

doi:10.1016/j.aim.2019.02.028

Cited by 4 publications

(19 citation statements)

References 29 publications

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“…From the product-quotient surface examples, we see that X 0 can have singular points other than nodal singularities. We can also see that X 0 can have singular points worse than quotient singularities from our previous work [31]. It will be very interesting if we can classify the classes of singularities of combinatorially minimal models of smooth minimal surfaces of general type with p g = 0.…”

Section: Introductionmentioning

confidence: 73%

“…In our previous paper [31], we provided several examples of Mori dream surfaces which are minimal surfaces of general type with p g = 0 and 2 ≤ K 2 ≤ 9. Indeed, it turns out that many classical or well-known surfaces of general type are Mori dream surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…First, we need some examples which show how the above procedures look like. In [31], we provided many examples of smooth projective Mori dream surfaces of general type with p g = 0 as follows.…”

Section: Introductionmentioning

confidence: 99%

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Combinatorially minimal Mori dream surfaces of general type

Keum¹,

Lee²

2022

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In this paper, we suggest a new approach to study minimal surfaces of general type with pg = 0 via their Cox rings, especially using the notion of combinatorially minimal Mori dream space introduced by Hausen in [22]. First, we study general properties of combinatorially minimal Mori dream surfaces. Then we discuss how to apply these ideas to the study of minimal surfaces of general type with pg = 0 which are very important but still mysterious objects. In our previous paper [31], we provided several examples of Mori dream surfaces of general type with pg = 0 and computed their effective cones explicitly. In this paper, we study their fibrations, explicit combinatorially minimal models and discuss singularities of the combinatorially minimal models. We also show that many minimal surfaces of general type with pg = 0 arise from the minimal resolutions of combinatorially minimal Mori dream surfaces.

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Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

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Combinatorially minimal Mori dream surfaces of general type

Keum¹,

Lee²

2022

Preprint

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“…For example, it turns out that there are many examples of Mori dream surfaces of general type with p g = 0 (cf. [KL19]), e.g. every fake projective plane is a Mori dream surface.…”

Section: Introductionmentioning

confidence: 99%

“…Surfaces isogenous to a product divide naturally into two types: unmixed if G acts diagonally on the product, mixed if there are elements of G which exchange the two factors. Every surface isogenous to a product of unmixed type with p g = 0 carries two natural fibrations onto P 1 , and one can use these fibrations to show that these surfaces are Mori dream surfaces, see [KL19].…”

Section: Introductionmentioning

confidence: 99%