Question

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.

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'.

Question: what is the pushforward f_* ω_f ?

It should be trivial, and David Speyer's answer to my question here should answer this question, but I (and a few others I asked earlier) couldn't get it to work.

Answer 1

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.