A Supersingular K 3 Surface in Characteristic 2 and the Leech Lattice
نویسنده
چکیده
Let k be an algebraically closed field of characteristic 2. Consider F4 ⊂ k and P(F4) ⊂ P(k). Let P be the set of points and let P̌ be the set of lines in P(F4). Each set contains 21 elements, each point is contained in exactly 5 lines, and each line contains exactly 5 points. It is known that the group of automorphisms of the configuration (P, P̌) is isomorphic to M21 ·D12, where M21(∼ = PSL(3,F4)) is a simple subgroup of the Mathieu group M24 and D12 is a dihedral group of order 12. In this paper, we prove the following main theorem.
منابع مشابه
ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC
We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.
متن کاملUnirationality of certain supersingular K 3 surfaces in characteristic 5
We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.
متن کاملSupersingular K3 Surfaces in Characteristic 2 as Double Covers of a Projective Plane
For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of P defined by w = G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a mo...
متن کاملTranscendental Lattices and Supersingular Reduction Lattices of a Singular K3 Surface
A (smooth) K3 surface X defined over a field k of characteristic 0 is called singular if the Néron-Severi lattice NS(X) of X ⊗ k is of rank 20. Let X be a singular K3 surface defined over a number field F . For each embedding σ : F →֒ C, we denote by T (Xσ) the transcendental lattice of the complex K3 surface Xσ obtained from X by σ. For each prime ideal p of F at which X has a supersingular red...
متن کاملLines in Supersingular Quartics
We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.
متن کامل