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Nodal Curves on K3 Surfaces
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abstract
In this paper, we study the Severi variety $V_{L,g}$ of genus $g$ curves in $|L|$ on a general polarized K3 surface $(X,L)$. We show that the closure of every component of $V_{L,g}$ contains a component of $V_{L,g-1}$. As a consequence, we see that the general members of every component of $V_{L,g}$ are nodal.
Forward citations
Cited by 1 Pith paper
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The Geometric Syzygy Conjecture in Positive Characteristic
The Geometric Syzygy Conjecture holds for general canonical curves over algebraically closed fields of characteristic at least 2g-4.
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