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Une sextique de l'espace projectif réel avec un grand nombre d'anses.

Frédéric Bihan — 2001

Revista Matemática Complutense

It follows from the known restrictions on the topology of a real algebraic variety that the number of handles of the real part of a real nonsingular sextic in CP is at most 47. We construct a real nonsingular sextic X in CP whose real part RX has 44 handles. In particular, this surface verifies b(RX) = h(X) + 2. We extend the construction in order to obtain for any even m ≥ 6 a real nonsingular surface X of degree m in CP verifying b(RX) > h(X). It is known that such a surface does not exist...

Gale duality for complete intersections

Frédéric Bihan;  Frank Sottile — 2008

Annales de l’institut Fourier

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...

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