On the irreducibility of Severi varieties on 𝐾3 surfaces

DOI10.1090/proc/14559zbMath1423.14192arXiv1809.03914OpenAlexW2962741488MaRDI QIDQ5232921

Thomas Dedieu, Ciro Ciliberto

Publication date: 13 September 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.03914

zbMATH Keywords

\(K3\) surfaceprincipal polarizationnodal curveSeveri variety

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Families, moduli of curves (analytic) (14H15)

Related Items (5)

Severi varieties on blow‐ups of the symmetric square of an elliptic curve ⋮ Nodal elliptic curves on \(K3\) surfaces ⋮ The Severi problem for abelian surfaces in the primitive case ⋮ On the irreducibility of the Severi variety of nodal curves in a smooth surface ⋮ On the automorphisms of Mukai varieties

Cites Work

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• Severi varieties and Brill-Noether theory of curves on abelian surfaces
• Brill-Noether theory on singular curves and torsion-free sheaves on surfaces
• On \(k\)-gonal loci in Severi varieties on general \(K3\) surfaces and rational curves on hyperkähler manifolds
• Weakly defective varieties
• Deformations of Algebraic Schemes
• Enumerating curves on rational surfaces: the rational fibration method
• Irreducibility of equisingular families of curves
• The universal Severi variety of rational curves on K3 surfaces
• Algebraic Families on an Algebraic Surface
• On \(k\)th-order embeddings of \(K3\) surfaces and Enriques surfaces

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