Limits of pluri-tangent planes to quartic surfaces

2013/04/28 by Ciliberto, Ciro, Dedieu, Thomas
#14D06 (Primary) 14J28 #14H50 #14N10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.7463

Abstract

We describe, for various degenerations S→ Δ of quartic K3 surfaces over the complex unit disk (e.g., to the union of four general planes, and to a general Kummer surface), the limits as t∈ Δ^* tends to 0 of the Severi varieties V_δ(S_t), parametrizing irreducible δ-nodal plane sections of S_t. We give applications of this to (i) the counting of plane nodal curves through base points in special position, (ii) the irreducibility of Severi varieties of a general quartic surface, and (iii) the monodromy of the universal family of rational curves on quartic K3 surfaces.

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