Which curves cut the Hyperelliptic locus? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T19:24:13Z http://mathoverflow.net/feeds/question/117797 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/117797/which-curves-cut-the-hyperelliptic-locus Which curves cut the Hyperelliptic locus? Jack 2013-01-01T18:29:57Z 2013-01-01T19:11:22Z <p>Consider the moduli space <code>$\mathcal{A}_{g,n}$</code> of abelian varieties with some level $n \geq 3$ structure. For simplicity, we just denote it by <code>$\mathcal{A}_{g}$</code> and drop $n$. Denote the locus of hyperelliptic Jacobians by $H_{g}$ (i.e. the image of hyperelliptic curves under the Torelli map). Now, having a curve $C$ in <code>$\mathcal{A}_{g}$</code>, are there necessary and/or sufficient results to determine whether $C$ intersects $H_{g}$ ?(I am particularly interested in the case where <code>$g=4$</code>)</p>