Poincaré Duality for Singular Tropical Hypersurfaces
Analysis
This paper extends Poincaré duality to a specific class of tropical hypersurfaces constructed via combinatorial patchworking. It introduces a new notion of primitivity for triangulations, weaker than the classical definition, and uses it to establish partial and complete Poincaré duality results. The findings have implications for understanding the geometry of tropical hypersurfaces and generalize existing results.
Key Takeaways
- •Extends Poincaré duality to a specific class of tropical hypersurfaces.
- •Introduces a new, weaker notion of primitivity for triangulations.
- •Establishes partial and complete Poincaré duality results based on primitivity.
- •Generalizes existing results and has implications for understanding tropical geometry.
Reference
“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”