On singularities of threefold weighted blowups

Chen, Yifei

doi:10.48550/arxiv.1911.04726

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2019

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“…Very recently Y. Chen [7] has proved Conjecture 1.2 for the case d = 3. We also refer to [7] for a more detailed explanation of the problem in the context of birational geometry.…”

Section: Introductionmentioning

confidence: 99%

Blowups with log canonical singularities

Sankaran,

Santos

2019

Preprint

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Using only elementary toric methods and facts about quotient singularities and lattice simplices, we show that for any fixed dimension d there is a constant ℓ d such that if a weighted blowup of A d has only canonical singularities then the smallest of the weights cannot exceed ℓ d . This is a special case of a conjecture of Birkar.Using the recent classification of 4-dimensional empty simplices by Iglesias-Valiño and Santos, we show that for blowups of A 4 with terminal singularities the smallest weight is at most 32, and at most 6 in all but finitely many cases.

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“…Very recently Y. Chen [7] has proved Conjecture 1.2 for the case d = 3. We also refer to [7] for a more detailed explanation of the problem in the context of birational geometry.…”

Section: Introductionmentioning

confidence: 99%