On the Shafarevich conjecture for irreducible symplectic varieties

2022/01/03 by Teppei Takamatsu, Takamatsu, Teppei
Mathematics · #11G35 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.00482

openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the Shafarevich conjecture for irreducible symplectic varieties of fixed deformation class. We also observe that the second cohomological generalization of the Shafarevich conjecture does not hold in general, and discuss another formulation of a cohomological generalization.

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