A generic global Torelli theorem for certain Horikawa surfaces

2017/02/20 by Gregory Pearlstein, Zheng Zhang, Pearlstein, Gregory +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1702.06204

openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Algebraic surfaces of general type with q=0, p_g=2 and K²=1 were described by Enriques and then studied in more detail by Horikawa. In this paper we consider a 16-dimensional family of special Horikawa surfaces which are certain bidouble covers of ℙ². The construction is motivated by that of special Kunev surfaces which are counterexamples for infinitesimal Torelli and generic global Torelli problem. The main result of the paper is a generic global Torelli theorem for special Horikawa surfaces. To prove the theorem, we relate the periods of special Horikawa surfaces to the periods of certain lattice polarized K3 surfaces using eigenperiod maps and then apply a Torelli type result proved by Laza.

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