Clifford’s Theorem for real algebraic curves
We establish, for smooth projective real curves, an analogue of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.
Codimension two transcendental submanifolds of projective space
We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
Complete decomposability of quotients by complex conjugation for real complete intersection surfaces.
Complex arrangements and derivations.
Complex orientation formulas for -curves of degree with 4 nests
On démontre la formule d’orientations complexes pour les -courbes dans de degré ayant nids. Cette formule généralise celle pour les -courbes à nid profond. C’est un pas vers la classification des -courbes de degré .
Complexifications of nonnegatively curved manifolds
Complexity of intersections of real quadrics and topology of symmetric determinantal varieties
Computing amoebas.
Construction d'hypersurfaces réelles
Cycles on algebraic models of smooth manifolds
Every compact smooth manifold is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of . We study modulo 2 homology classes represented by algebraic subsets of , as runs through the class of all algebraic models of . Our main result concerns the case where is a spin manifold.