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{
    "pk": 64948,
    "title": "An Ehrhart theory for tautological intersection numbers",
    "subtitle": null,
    "abstract": "We discover that tautological intersection numbers on \\(\\overline{\\mathcal{M}}_{g, n}\\), the moduli space of stable genus \\(g\\) curves with \\(n\\) marked points, are evaluations of Ehrhart polynomials of partial polytopal complexes. In order to prove this, we realize the Virasoro constraints for tautological intersection numbers as a recursion for integer-valued polynomials. Then we apply a theorem of Breuer that classifies Ehrhart polynomials of partial polytopal complexes by the nonnegativity of their \\(f^*\\)-vector. In dimensions 1 and 2, we show that the polytopal complexes that arise are inside-out polytopes i.e. polytopes that are dissected by a hyperplane arrangement.\n \nMathematics Subject Classifications: 14H10, 52B20\n \nKeywords: Moduli of curves, Ehrhart polynomials",
    "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": "Moduli of curves"
        },
        {
            "word": "Ehrhart polynomials"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5m02m61r",
    "frozenauthors": [
        {
            "first_name": "Adam",
            "middle_name": "",
            "last_name": "Afandi",
            "name_suffix": "",
            "institution": "Mathematics Münster, Universität Münster, Münster, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2024-09-26T15:50:12+02:00",
    "date_accepted": "2024-09-26T15:50:12+02:00",
    "date_published": "2024-09-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64948/galley/49758/download/"
        }
    ]
}