We discuss a tropical approach to enumeration of singular complex and real hypersurfaces in toric varieties. In particular, we establish a correspondence theorem between singular tropical and algebraic hypersurfaces and demonstrate a multi-dimensional version of a lattice path algorithm. As application we obtain a lower bound to the maximal possible number of real singular hypersurfaces in a generic real pencil.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5968