Geodesic
Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
Philipp Jell1 ; Hannah Markwig2 ; Felipe Rincón3 ; Benjamin Schröter4
1University of Regensburg
2Eberhard Karls Universität Tübingen
3Queen Mary University of London
4KTH Stockholm
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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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.
DOI : 10.37236/10674
Classification : 14T15, 14T20, 05B35, 14M15
Mots-clés : tropical geometry, matroid theory, valuated matroid theory

Philipp Jell  1   ; Hannah Markwig  2   ; Felipe Rincón  3   ; Benjamin Schröter  4

1 University of Regensburg
2 Eberhard Karls Universität Tübingen
3 Queen Mary University of London
4 KTH Stockholm 
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     title = {Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/10674},
     zbl = {1492.14109},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10674/}
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Philipp Jell; Hannah Markwig; Felipe Rincón; Benjamin Schröter. Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10674

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