Combinatorial patchworking in codimension 2 and more (Enzo Pasquereau, Université de Nantes)

13.10.2025 14:00 – 16:00

Abstract:
Combinatorial patchworking is a powerful method used for constructing real algebraic hypersurfaces with controlled topology. I will discuss generalization of this method to higher codimension using real phase structure. In codimension 2, we give explicit patchworking rules (based on triangulations, sign distributions, and edge orientations) similar to Viro's original formulation for hypersurface. As an application, we obtain families of maximal T-curves in real projective 3-space. For higher codimension, we derive new bounds on the number of connected components and prove non-existence of maximal T-curves (for codimension >3) and of high codimension T-surfaces.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Fables Géométriques"

entrée libre