Primitive real algebraic surfaces in 3-dimensional toric varieties (Aloïs DEMORY, Genève)

20.11.2024 14:00 – 16:00

Abstract:
The study of topology of real algebraic hypersurfaces is classically divided into two complementary directions : on one hand, finding restrictions on the topology of the real part of real algebraic hypersurfaces with given Newton polytope, and on the other hand, constructing real algebraic varieties with interesting topological properties of their real part. Primitive patchworking is a very fruitful combinatorial construction tool introduced by O. Viro that allowed to construct many maximal (with respect to the Smith-Thom inequality) real algebraic hypersurfaces in various smooth ambient spaces.
The very specific topological properties of the hypersurfaces produced using this method are quite well studied in the case of hypersurfaces in smooth toric varieties. We present an ongoing attempt to extend some of these properties to primitive surfaces in arbitrary 3-dimensional toric varieties. As a consequence, new maximal surfaces in certain singular and non-singular toric 3-folds are constructed.

Lieu

Bâtiment: Conseil Général 7-9

Room 6-13, Seminaire "Fables géométriques"

entrée libre