On the irreducibility of Severi varieties on K3 surfaces

2018/09/11 by Ciro Ciliberto, Thomas Dedieu, Ciliberto, Ciro +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1809.03914

openalex publication_date 2018/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (S,L) be a polarized K3 surface of genus p \geqslant 11 such that Pic(S)=Z[L], and δ a non-negative integer. We prove that if p\geqslant 4δ-3, then the Severi variety of δ-nodal curves in |L| is irreducible.

Citations

• Algebraic Families on an Algebraic Surface

Cited by

• Severi varieties on Enriques surfaces of base change type and on rational elliptic surfaces

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