# Perfect points on genus one curves and consequences for supersingular K3 surfaces

@article{Bragg2019PerfectPO, title={Perfect points on genus one curves and consequences for supersingular K3 surfaces}, author={Daniel Bragg and Max Lieblich}, journal={arXiv: Algebraic Geometry}, year={2019} }

We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus one curves over function fields admit no points over the perfect closure of the base field) and use it to show that any non-Jacobian elliptic structure on a very general supersingular K3 surface has no purely inseparable multisections. We also describe specific examples of such fibrations without purely inseparable multisections. Finally, we discuss the…

## 5 Citations

Supersingular O’Grady Varieties of Dimension Six

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O'Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this paper, we naturally…

Supersingular Irreducible Symplectic Varieties

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We study symplectic varieties defined over fields of positive characteristics, especially the supersingular ones, generalizing the theory of supersingular K3 surfaces. In this work, we are mainly…

Pell surfaces

- MathematicsActa Mathematica Hungarica
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In 1826 Abel started the study of the polynomial Pell equation x 2 − g ( u ) y 2 = 1. Its solvability in polynomials x ( u ), y ( u ) depends on a certain torsion point on the Jacobian of the…

Ordinary varieties with trivial canonical bundle are not uniruled

- MathematicsMathematische annalen
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It is proved that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic minimal are not geometrically uniruled and the singular version of the theorem is shown, which is sharp in multiple aspects.

Correction to: Supersingular K3 surfaces are unirational

- PhysicsInventiones mathematicae
- 2021

As was pointed out by Bragg and Lieblich

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