Degree two curves in $C^{(2)}$
Year: 2015
Type: preprint
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 $C\times C$.
Source: arXiv (Cornell University)
Author: Sáez, Meritxell
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1538845668