53 citations · 163 across the 21 of their papers we have counts for
6 papers · 1 filter
Superforms, Tropical Cohomology, and Poincaré Duality
Philipp Jell, Kristin Shaw, Jascha Smacka
We establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we pro…
Non-existence of hypersurfaces with real fibered logarithmic Gauss map
Kristin Shaw
This submission has been withdrawn and replaced with the paper "Non-existence of torically maximal hypersurfaces" arXiv:1506.02813.
Tropical Hopf manifolds and contracting germs
Matteo Ruggiero, Kristin Shaw
Classical Hopf manifolds are compact complex manifolds whose universal covering is . We investigate the tropical analogues of Hopf manifolds, and rela…
Tropical surfaces
Kristin Shaw
We present tools and definitions to study abstract tropical manifolds in dimension 2, which we call simply tropical surfaces. This includes explicit descriptions of intersection nu…
Non-existence of torically maximal hypersurfaces
Erwan Brugallé, Grigory Mikhalkin, Jean-Jacques Risler +1
Torically maximal curves (known also as simple Harnack curves) are real algebraic curves in the projective plane such that their logarithmic Gauß map is totally real. In this paper…
Brief introduction to tropical geometry
Erwan Brugallé, Ilia Itenberg, Grigory Mikhalkin +1
The paper consists of lecture notes for a mini-course given by the authors at the Gökova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves i…