REVIEW 3 cited by
Tropical Vector Bundles
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
read the original abstract
The goal of this paper is to introduce a construction of a vector bundle on a tropical variety. When the base is a tropical toric variety these tropicalize toric vector bundles, and are described by the data of a valuated matroid and some flats in the lattice of flats of the underlying matroid. The fibers are tropical linear spaces. We define global sections for tropical toric vector bundles, stability, and Jordan-H\"older and Harder-Narasimhan filtrations. Many of these require additional modularity assumptions on the defining matroid.
Forward citations
Cited by 3 Pith papers
-
On Ehrhart theory for tropical vector bundles
Each tropical vector bundle carries a convex chain whose values equal its equivariant Euler characteristic, yielding a combinatorial Riemann–Roch formula; for the tautological bundle of a matroid, the Euler characteri...
-
Vector-valued Laurent polynomial equations, toric vector bundles and matroids
A vector-valued BKK theorem: generic zeros of a torus-invariant vector-valued Laurent polynomial are counted by the mixed volume of virtual polytopes delta_i - delta_{i-1}, and the associated mixed volumes satisfy an ...
-
Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves
The authors prove that pointed matroids over perfect idylls form a combinatorial proto-exact category with duality and exact direct sum, and that tropical toric reflexive sheaves (modular ones in particular) are proto...
Discussion (0). Continue with ORCID to comment.