Non-Emptiness of the Height Strata of the Moduli Stack of Polarized K3 Surfaces

Details Non-Emptiness of the Height Strata of the Moduli Stack of Polarized K3 Surfaces Non-Emptiness of the Height Strata of the Moduli Stack of Polarized K3 Surfaces

2005-06-14

arxiv.org/abs/math/0506271v1

Mathematics

Algebraic Geometry

15 pages, LaTeX

Scientific paper

In this paper we consider the following problem: For a given natural number $d$ and a prime $p$ determine all Newton polygons of polarized K3 surfaces of degree 2d over fields of characteristic $p$. This is an analogue of the Manin problem for Newton polygons of abelian varieties. This question is equivalent to determining the non-empty height strata of the moduli stack $\M_{2d}\otimes \F_p$ of K3 surfaces with a polarization of degree 2d over $\F_p$. We prove here that if $d$ is large enough and prime to $p$, then the height strata of $\M_{2d}\otimes \F_p$ are non-empty.

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