Moduli Spaces of Codimension-One Subspaces in a Linear Variety and their Tropicalization
| Autor: | Philipp Jell, Hannah Markwig, Felipe Rincón, Benjamin Schröter |
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| Rok vydání: | 2022 |
| Předmět: |
Mathematics::Combinatorics
Applied Mathematics Theoretical Computer Science Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 14T15 14T20 05B35 14M15 Computational Theory and Mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Geometry and Topology Algebraic Geometry (math.AG) Physics::Atmospheric and Oceanic Physics |
| Zdroj: | The Electronic Journal of Combinatorics. 29 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/10674 |
| Popis: | We study the moduli space of $d$-dimensional linear subspaces contained in a fixed $(d+1)$-dimensional linear variety $X$, and its tropicalization. We prove that these moduli spaces are linear subspaces themselves, and thus their tropicalization is completely determined by their associated (valuated) matroids. We show that these matroids can be interpreted as the matroid of lines of the hyperplane arrangement corresponding to $X$, and generically are equal to a Dilworth truncation of the free matroid. In this way, we can describe combinatorially tropicalized Fano schemes and tropicalizations of moduli spaces of stable maps of degree $1$ to a plane. 30 pages, 9 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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