Séminaire de Géométrie Tropicale
Mercredi 08 octobre, 16h15 salle 1525-502
Enumeration of singular tropical hypersurfaces
Résumé :
Singular hypersurfaces of a given degree in a toric
variety, associated with a non-degenerate convex lattice polytope,
can be enumerated via the algebraic-tropical correspondence theorem
established by H. Markwig, T. Markwig and the author. We describe this
correspondence, determine weights of singular tropical hypersurfaces,
and explain the multi-dimensional lattice path algorithm, which
appears to be rather involved as compared with the algorithm for
plane tropical curves. In some special cases, the lattice path
algorithm converts into a floor decomposition algorithm.
Joint work with H. and T. Markwig.