mercoledi' 29-03-2006 (15:30) - Sala Seminari Priska Jahnke (Bayreuth) : Terminal Fano threefolds and their smoothings
Argomento: Geometria
Abstract:
Let X be a Gorenstein Fano threefold with at most canonical singularities. It is known, that there are only finitely many deformation families of such X, so one may ask for a complete classification as was done in thesmooth case by Iskovskikh, Mori and Mukai. An important question is under which conditions X arises as a degeneration of a smooth Fano threefold, and if that is the case, how X and its "smoothing" are related. In 1997 Namikawa proved the existence of a smoothing, if X has only terminal singularities, i.e., X is the special fiber of a flat family Z -> D with general fiber Z_t a smooth Fano threefold. Here Z is an irreducible complex space, not necessarily smooth. We show that the Picard groups of X and Z_t are isomorphic in the terminal case and give some examples concerning canonical singularities. Here a smoothing need notexist, and even if it exists, the Picard number may jump.
Segreteria Didattica Giulia Curciarello tel- 050 2213219
_______________________________________________ Settimanale mailing list Settimanale@mail.dm.unipi.it https://mail.dm.unipi.it/mailman/listinfo/settimanale