Tropical positivity and determinantal varieties
Copyright policy )Tropical positivity and determinantal varieties
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We focus on the study of low-rank matrices, in particular matrices of rank 2 and 3 . Moreover, in the case of square-matrices of corank 1 , we fully classify the signed tropicalization of the determinantal variety, even beyond the positive part.
- University of Twente Netherlands
signed tropicalization, Birkhoff polytope, Combinatorial aspects of algebraic geometry, Determinantal varieties, Combinatorial aspects of tropical varieties, positive-tropical generators, Real algebraic sets, Mathematics - Algebraic Geometry, 14T15, 14P05, 14M12, 05E14 (Primary) 52B40 (Secondary), bicolored phylogenetic trees, FOS: Mathematics, Mathematics - Combinatorics, determinantal varieties, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Algebraic Geometry (math.AG)
signed tropicalization, Birkhoff polytope, Combinatorial aspects of algebraic geometry, Determinantal varieties, Combinatorial aspects of tropical varieties, positive-tropical generators, Real algebraic sets, Mathematics - Algebraic Geometry, 14T15, 14P05, 14M12, 05E14 (Primary) 52B40 (Secondary), bicolored phylogenetic trees, FOS: Mathematics, Mathematics - Combinatorics, determinantal varieties, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Algebraic Geometry (math.AG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!