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

2005/06/14 by Jordan Rizov, Rizov, Jordan
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0506271

15 pages, LaTeX

arxiv created 2005/06/14 · openalex publication_date 2005/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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⊗ \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⊗ \F_p are non-empty.

Citations

• Moduli Stacks of Polarized K3 Surfaces in Mixed Characteristic

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