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arXiv · 1905.07116

On the irreducibility of the Severi variety of nodal curves in a smooth surface

Edoardo Ballico
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Abstract

Let $X$ be a smooth projective surface and $L\in \mathrm{Pic}(X)$. We prove that if $L$ is $(2k-1)$-spanned, then the set $\tilde{V}_k(L)$ of all nodal and irreducible $D\in |L|$ with exactly $k$ nodes is irreducible. The set $\tilde{V}_k(L)$ is an open subset of a Severi variety of $|L|$, the full Severi variety parametrizing all integral $D\in |L|$ with geometric genus $g(L)-k$.

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Edoardo Ballico. 2019-05-17. On the irreducibility of the Severi variety of nodal curves in a smooth surface. https://arxiv.org/abs/1905.07116

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