Unirationality of certain supersingular K3 surfaces in characteristic 5

Pho, Duc Tai; Shimada, Ichio

doi:10.1007/s00229-006-0045-3

Cited by 9 publications

(3 citation statements)

References 20 publications

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“…Shioda [Sh77b] established this conjecture for supersingular Kummer surfaces in odd characteristic, Rudakov and Sharafevich [RS78] showed it in characteristic 2 and for K3 surfaces with Artin invariant σ 0 ≤ 6 in characteristic 3, and Pho and Shimada [PS06] for K3 surfaces with Artin invariant σ 0 ≤ 3 in characteristic 5. We refer to [Ka87] and [I-L13] for some refinements.…”

Section: Introductionmentioning

confidence: 94%

Supersingular K3 surfaces are unirational

Liedtke

2014

Invent. math.

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ABSTRACT. We show that supersingular K3 surfaces in characteristic p ≥ 5 are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda. As a byproduct, we exhibit the moduli space of rigidified K3 crystals as an iterated P 1 -bundle over F p 2 . To complete the picture, we also establish Shioda-Inose type isogeny theorems for K3 surfaces with Picard rank ρ ≥ 19 in positive characteristic.

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Section: Introductionmentioning

confidence: 94%

Supersingular K3 surfaces are unirational

Liedtke

2014

Invent. math.

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“…It mimics a construction of Pho and Shimada [Pho and Shimada 2006] for unirational K3 surfaces in characteristic 5.…”

Section: Families Of Unirational Horikawa Surfacesmentioning

confidence: 99%

Unirational surfaces on the Noether line

Liedtke¹,

Schütt²

2009

Pacific J. Math.

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“…In [Pho and Shimada 2006], it is shown that every supersingular K 3 surface in characteristic 5 with Artin invariant ≤ 3 is obtained as a double cover of the projective plane with the branch curve defined by y 5 − f (x) = 0, where f (x) is a polynomial of degree 6, and hence it is unirational.…”

Section: Proof Of Main Theoremmentioning

confidence: 99%