most recent 30 from http://mathoverflow.net 2013-05-19T16:34:11Z http://mathoverflow.net/feeds/question/117087 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/117087/is-the-moduli-space-of-genus-three-smooth-quartics-affine Masse 2012-12-23T13:36:21Z 2012-12-23T13:36:21Z

<p>Non-hyperelliptic curves of genus three are smooth quartics. Is the moduli space of such curves affine?</p> <p>I think this follows from a more general result on smooth complete intersections, but I'm looking for a simple proof.</p> <p>One idea would be to use a "good" compactification, i.e., such that the boundary divisor is ample. This can be done by using a suitable Grassmannian containing the Hilbert scheme. </p> <p>I'd like to avoid something like this and give a more elementary argument. Is that possible?</p>