Timeline for Has anyone studied the Prym map for double covers with two ramification points?

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Jun 24, 2011 at 16:58	comment	added	roy smith		yes, Beauville's theory (and earlier partial steps by Masiewicki) shows that double covers with an even number of ramification points do yield a ppav once one identifies those points in pairs. But this does not help solve the ramified torelli problem since the torelli results for Beauville pryms are so generic, that the injectivity does not specialize. for covers that become singular so as to be still unramified however one can use induction on the normalization once that normalization becomes generic. Bob Friedman and I took this inductive approach to generic torelli for plane septics.
Jun 24, 2011 at 4:44	comment	added	Dan Petersen		Thanks for the insight, this seems like a useful perspective. I guess another way of saying this is that you are identifying $R_{g,2}$ with a boundary stratum of the space $\overline{R}_{g+1}$ of admissible covers, and hence the two-pointed prym map with the restriction of the ordinary prym map in genus g+1.
Jun 23, 2011 at 22:38	history	edited	roy smith	CC BY-SA 3.0	added 160 characters in body; added 21 characters in body
Jun 23, 2011 at 22:16	history	edited	roy smith	CC BY-SA 3.0	added 4 characters in body
Jun 23, 2011 at 22:00	history	answered	roy smith	CC BY-SA 3.0