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No abstract uploaded!

No abstract uploaded!

Characteristic numbers of families of maps of nodal curves to$P$^{2}are defined as intersection of natural divisor classes. (This definition agrees with the usual definition for families of plane curves.) Simple recursions for characteristic numbers of genus one plane curves of all degrees are computed.

A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature polyhedral metric which is unique up to scaling. Furthermore, the constant curvature metric can be found using a discrete Yamabe flow with surgery.