REVIEW 1 cited by
Homological smoothness and Deligne resolution for tropical fans
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We say that a tropical fan is homologically smooth if each of its open subsets verify tropical Poincare duality. A tropical homology manifold is a tropical variety that is locally modelled by open subsets of homologically smooth tropical fans. We show that homological smoothness is a T-stable property in the category of tropical fans. This implies in particular that quasilinear fans are homologically smooth, and tropical varieties locally modelled by them are tropical homology manifolds. Previously, this was known only for locally matroidal tropical varieties. In order to show the above results, we prove a tropical analogue of the Deligne weight spectral sequence for homologically smooth tropical fans. This allows to describe the cohomology of tropical modifications, and will be of importance in our companion work which develops a Hodge theory in the tropical setting.
Forward citations
Cited by 1 Pith paper
-
Tropical Abel-Jacobi theory
A functorial Abel-Jacobi map is constructed for all compact tropical varieties, and the tropical Ceresa class of a curve is computed explicitly from the graph and edge lengths.
Discussion (0). Continue with ORCID to comment.