215 citations · 640 across the 23 of their papers we have counts for
11 papers · 1 filter
A specialization inequality for tropical complexes
Dustin Cartwright
We prove a specialization inequality relating the dimension of the complete linear series on a variety to the tropical complex of a regular semistable degeneration. Our result exte…
Excluded homeomorphism types for dual complexes of surfaces
Dustin Cartwright
We study an obstruction to prescribing the dual complex of a strict semistable degeneration of an algebraic surface. In particular, we show that if is a complex homeomorphic to…
Lifting matroid divisors on tropical curves
Dustin Cartwright
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves…
Lifting divisors on a generic chain of loops
Dustin Cartwright, David Jensen, Sam Payne
Let C be a curve over a complete valued field with infinite residue field whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of lo…
Tropical complexes
Dustin Cartwright
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, a…
The Gröbner stratification of a tropical variety
Dustin Cartwright
Each Gröbner stratum of a tropical variety is a connected set of points, all of which induce the same initial subscheme. The Gröbner stratification is a coarsening of the decomposi…