most recent 30 from http://mathoverflow.net 2010-03-11T15:09:20Z http://mathoverflow.net/feeds/question/3913 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/3913/triviality-of-the-hodge-bundle-for-a-special-family-of-semistable-curves David Brown 2009-11-03T07:18:22Z 2009-11-03T07:32:42Z

<p>Let g,h be positive integers. Let E be an elliptic curve, C be a genus h curve, and D be a genus g-h-1 curve. Let c,d,e be points on (resp.) C,D, and E. </p> <p>Let f:CC --> E-e be the family whose fiber over a point e' is the curve obtained by glueing C to E together at the points c and e and D to E at the points d and e'. </p> <blockquote> <p>Question: what is the pushforward f_* &omega;_f ?</p> </blockquote> <p>It should be trivial, and David Speyer's answer to my question <a href="http://mathoverflow.net/questions/2107/question-about-a-family-of-semistable-curves/2145#2145" rel="nofollow">here</a> should answer this question, but I (and a few others I asked earlier) couldn't get it to work.</p>

http://mathoverflow.net/questions/3913/triviality-of-the-hodge-bundle-for-a-special-family-of-semistable-curves/3914#3914 David Lehavi 2009-11-03T07:32:42Z 2009-11-03T07:32:42Z

<p>Under (the extension of) Torrelli this curves maps to one point in Ag. On the other hand the hodge class on Mg minus D0 is a pullback (under the extension of Torelli) of the hodge class on Ag.</p>