Supersingular K3 surfaces are unirational
By C. Liedtke. 2013
50 citations recorded by the source corpus.
We show that supersingular K3 surfaces in characteristic $$p\ge 5$$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 $${{\mathbb P}}^1$$P1-bundle over $${{\mathbb F}}_{p^2}$$Fp2. To complete the picture, we also establish Shioda–Inose type isogeny theorems for K3 surfaces with Picard rank $$\rho \ge 19$$ρ≥19 in positive characteristic.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/44ac6f82117323ca60cb79898a2dfe14962c55db
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In Geometry and Topology
- D. Huybrechts
- Claire Voisin
- Kieran G. O’Grady
- E. Markman
- P. Stellari
- Ulrike Riess
- G. Farkas
- Emanuele Macrì
In Mathematical Physics
- D. Huybrechts
- Claire Voisin
- P. Stellari
- E. Markman
- Emanuele Macrì
- Ulrike Riess
- Alexander Perry
- G. Farkas
Citations in the corpus
- Lectures on K3 Surfaces (2016, background): “The converse has recently been proved by Liedtke in [371], answering a question by Artin in [16, p.”
- Curves and cycles on K3 surfaces (2013, background): “he converse has recently be completed in [Cha12, Mau12, Ma13]. (It has also been known that unirational K3 surfaces are Shioda (and hence Artin) supersingular and the converse has been established in [Li13].) Thus, a K3 surface X over k with char(k) 6= 2 is supersingular if and only if ρ(X) 6= 22 , ”