Linear Spaces, Buildings and Principal Bundles on Curves in Tropical Geometry

Q: What does this research mean for the field?

The Bruhat-Tits building of PGLr+1(K) arises as the inverse limit of all tropicalized linear spaces, and tropical principal bundles on metric graphs can be classified analogously to classical algebraic bundles. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

Arne Kuhrs

doi:10.17619/unipb/1-2573

May 26, 2026Open Access

Linear Spaces, Buildings and Principal Bundles on Curves in Tropical Geometry

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Key Points

The aim is to establish new connections between tropical linear spaces, Bruhat-Tits buildings, and valuated matroids, while developing a tropical theory of principal bundles on curves.
Developed tropical interpretations of buildings for the projective general linear group
Introduced signed Goldman-Iwahori spaces and their real tropical counterparts
Constructed tropical analogs of reductive groups and classified tropical principal bundles on metric graphs
Identified the essential skeleton of the moduli space of semistable bundles on a Tate curve with its tropical counterpart
Demonstrated the equivalence of the signed Goldman-Iwahori space with the real tropical linear space of a universal realizable oriented matroid
Extended the construction of tropical linear spaces to valuated matroids with infinite ground sets

Implication

This dissertation explores connections between tropical linear structures and principal bundles on curves, implying new approaches to geometry.

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Cite This Study

Arne Kuhrs (2026) studied this question.

synapsesocial.com/papers/6a1a80c00307b78509432afa https://doi.org/10.17619/unipb/1-2573

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Linear Spaces, Buildings and Principal Bundles on Curves in Tropical Geometry

Key Points

Implication

Abstract

Discussion

Cite This Study

Linear Spaces, Buildings and Principal Bundles on Curves in Tropical Geometry

Key Points

Implication

Abstract

Discussion

Cite This Study

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