Primitive combinatorial patchworking under relaxed hypotheses
Date(s) : 13/02/2025 iCal
11h00 - 12h00
Primitive combinatorial patchworking is a combinatorial method introduced by O. Viro that allows one to obtain real algebraic hypersurfaces starting from a convex triangulation of a convex polytope together with signs on the vertices of the triangulation. Over the years, it was used to construct many examples of topologically interesting non-singular real algebraic hypersurfaces in various ambient spaces.
The non-singular hypersurfaces produced using this method have very specific topological properties that are quite well understood when the polytope corresponds to a smooth toric variety, and it turns out that these properties persist even when the triangulation is not convex. One can then wonder if similar properties can also be observed under more relaxed hypotheses: what if the polytope corresponds to a singular toric variety ? what if, instead of polytopes, we consider triangulations of more general objects ?
We describe some very partial answers to these questions, with an emphasis on the case of surfaces in three-dimensional ambient spaces.
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