Rational curves on K3 surfaces of small genus

2020/11/20 by Rijul Saini, Saini, Rijul
Mathematics · #14H45 (Secondary) #14J28 (Primary) #20B25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2011.10181

openalex publication_date 2020/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrak B_g denote the moduli space of primitively polarized K3 surfaces (S,H) of genus g over \mathbb C. It is well-known that \mathfrak B_g is irreducible and that there are only finitely many rational curves in |H| for any primitively polarized K3 surface (S,H). So we can ask the question of finding the monodromy group of such curves. The case of g=2 essentially follows from the results of Harris \citeHa to be the full symmetric group S₃₂₄, here we solve the case g=3 and 4.

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