most recent 30 from http://mathoverflow.net 2013-05-23T17:52:48Z http://mathoverflow.net/feeds/question/64128 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64128/projectivized-normal-cone-to-satake-compactification Charles Siegel 2011-05-06T14:07:33Z 2011-05-06T17:09:17Z

<p>Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties over $\mathbb{C}$.</p> <p>There exists a compactification, the Satake compactification, which is minimal and has the property that <code>$$\overline{\mathcal{A}}_g=\mathcal{A}_g\coprod\overline{\mathcal{A}}_{g-1}.$$</code></p> <p>It's well known that for a space in $\mathcal{A}_{g-1}$, the projectivized normal cone of the boundary in the whole thing is the Kummer of the point.</p> <p>What about the higher codimension strata? For instance, what is the projectivized normal cone at a point for the embedding $\overline{\mathcal{A}}_1\subset \overline{\mathcal{A}}_g$, or $\overline{\mathcal{A}}_2\subset \overline{\mathcal{A}}_g$?</p> <p>Is there a good general method for computing these?</p>