Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces
Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces
A complex variety, degenerating over a punctured disk, carries a limit mixed Hodge structure on its cohomology, encoding the action of monodromy. The associated limit mixed Hodge–Deligne polynomial can be expressed in terms of the motivic nearby fiber. Using techniques from tropical geometry, we present a new formula for the …