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{
    "pk": 64925,
    "title": "The spine of the \\(T\\)-graph of the Hilbert scheme of points in the plane",
    "subtitle": null,
    "abstract": "The torus \\(T\\) of projective space also acts on the Hilbert scheme of subschemes of projective space. The \\(T\\)-graph of the Hilbert scheme has vertices the fixed points of this action, and edges connecting pairs of fixed points in the closure of a one-dimensional orbit. In general this graph depends on the underlying field. We construct a subgraph, which we call the spine, of the \\(T\\)-graph of \\(\\operatorname{Hilb}^m(\\mathbb A^2)\\) that is independent of the choice of infinite field. For certain edges in the spine we also give a description of the tropical ideal, in the sense of tropical scheme theory, of a general ideal in the edge. This gives a more refined understanding of these edges, and of the tropical stratification of the Hilbert scheme.\n \nMathematics Subject Classifications: 14C05, 14T10, 14L30\n \nKeywords: Hilbert scheme, \\(T\\)-graph, tropical ideal",
    "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": "Hilbert scheme"
        },
        {
            "word": "\\(T\\)-graph"
        },
        {
            "word": "tropical ideal"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/74v009bx",
    "frozenauthors": [
        {
            "first_name": "Diane",
            "middle_name": "",
            "last_name": "Maclagan",
            "name_suffix": "",
            "institution": "Mathematics Institute, University of Warwick, Coventry, U.K.",
            "department": ""
        },
        {
            "first_name": "Rob",
            "middle_name": "",
            "last_name": "Silversmith",
            "name_suffix": "",
            "institution": "Mathematics Institute, University of Warwick, Coventry, U.K.",
            "department": ""
        }
    ],
    "date_submitted": "2024-06-28T13:41:00+02:00",
    "date_accepted": "2024-06-28T13:41:00+02:00",
    "date_published": "2024-06-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64925/galley/49735/download/"
        }
    ]
}