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arXiv · 1503.05143

Degree two curves in $C^{(2)}$

Meritxell Sáez
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Abstract

In this paper we give a precise classification of the pairs $(C,\widetilde{B})$ with $C$ a smooth curve of genus $g$ and $\widetilde{B}\subset C^{(2)}$ a curve of degree two and positive self-intersection. We prove that there are no such pairs if $g < p_a(\widetilde{B})< 2g-1$. We study the singularities and self-intersection of any degree two curve in $C^{(2)}$. Moreover, we give examples of curves with arithmetic genus in the Brill-Noether range and positive self-intersection on $C\times C$.

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Meritxell Sáez. 2015-03-17. Degree two curves in $C^{(2)}$. https://arxiv.org/abs/1503.05143

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