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Tropical Quiver Grassmannians

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arxiv 2311.18648 v1 pith:2INVZNF6 submitted 2023-11-30 math.CO math.AGmath.RT

Giulia Iezzi , Victoria Schleis This is my paper · ORCID
classification math.COmath.AGmath.RT
keywords quivertropicaldressiansgrassmanniansintroducematroidsparametrizespaces
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We introduce quivers of valuated matroids and study their tropical parameter spaces. We define quiver Dressians, which parametrize containment of tropical linear spaces after tropical matrix multiplication, and show that tropicalizations of quiver Grassmannians parametrize the realizable analogue. We further introduce affine morphisms of valuated matroids and show compatibility with weakly monomial quiver representations. Finally, we show that starting in ambient dimension 2, quiver Dressians can have nonrealizable points.

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Cited by 1 Pith paper

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  1. Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves

    math.CT 2025-09 conditional novelty 6.0 of 10

    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...

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