Gale duality for complete intersection

Frederic Bihan (1) , Frank Sottile (2)

1 LAMA - Laboratoire de Mathématiques
2 Department of Mathematics [Texas A&M University]

We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master functions and to compute some topological invariants of master function complete intersections.

Domaines: Géométrie algébrique [math.AG]

Frederic Bihan, Frank Sottile. Gale duality for complete intersection. Annales de l'Institut Fourier, 2008, 58 (3), pp.877-891. ⟨hal-00380182⟩