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{
    "pk": 64906,
    "title": "On the birational geometry of matroids",
    "subtitle": null,
    "abstract": "This paper investigates isomorphisms of Bergman fans of matroids respecting different fan structures, which we regard as matroid analogs of birational maps. We show that isomorphisms respecting the fine fan structure are induced by matroid isomorphisms.\nWe introduce Cremona automorphisms of the coarse structure of Bergman fans, which are not induced by matroid automorphisms. We show that the automorphism group of the coarse fan structure is generated by matroid automorphisms and Cremona maps in the case of rank \\(3\\) matroids which are not parallel connections and for modularly complemented matroids.\n \nMathematics Subject Classifications: 14T20, 52B40, 14E07\n \nKeywords: Matroids, birational geometry",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Matroids"
        },
        {
            "word": "birational geometry"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7t28108s",
    "frozenauthors": [
        {
            "first_name": "Kris",
            "middle_name": "",
            "last_name": "Shaw",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Oslo, Norway",
            "department": ""
        },
        {
            "first_name": "Annette",
            "middle_name": "",
            "last_name": "Werner",
            "name_suffix": "",
            "institution": "Goethe University Frankfurt, Institut für Mathematik, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-14T08:27:48Z",
    "date_accepted": "2023-09-14T08:27:48Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64906/galley/49716/download/"
        }
    ]
}