Tropical contractions to integral affine manifolds with singularities

Abstract: We construct contraction maps from tropical Calabi--Yau varieties to the integral affine manifolds with singularities that arise as the dual intersection complexes of toric degenerations of Calabi--Yau varieties in the Gross--Siebert program. We show that the contractions preserve tropical cohomology groups, and send the eigenwaves to the radiance obstructions. As an application, we also prove the Poincaré--Verdier duality for integral affine manifolds with singularities.

mathematical physicsalgebraic geometrycomplex variablesdifferential geometrygeometric topologyquantum algebrasymplectic geometry

Audience: researchers in the topic

Emmy Noether Kolloquium Mainz