Cohomology of toric varieties and tropical calculus
by
Andras Szenes
Mathematics Institute, BME, Budapest
Coauthors: Michele Vergne (Ecole Politechnique)

Given an orbifold toric variety obtained as a quotient of a vector space by a torus, we construct an explicit real complete intesection cycle in the complement of a hyperplane arrangement of the Lie algebra of this torus. The cycle represents the intersection pairing of the toric variety via a residue integral. The proof of the formula uses real algebraic degeneration methods related to "tropical calculus".