Phase tropical hypersurfaces

TL;DR

This paper proves that generic smooth complex hypersurfaces in the complex torus are topologically equivalent to their phase tropical counterparts, establishing a deep connection between complex geometry and tropical geometry.

Contribution

It introduces a topological equivalence between smooth complex hypersurfaces and phase tropical hypersurfaces, advancing the understanding of their geometric relationship.

Findings

Generic smooth complex hypersurfaces are homeomorphic to phase tropical hypersurfaces.

Establishes a topological correspondence between complex and tropical geometries.

Provides new insights into the structure of complex hypersurfaces in the torus.

Abstract

We prove that a generic smooth complex hypersurface in the complex torus is homeomorphic to the corresponding phase tropical hypersurface.