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dc.contributor.authorRanganathan, D
dc.contributor.authorUsatine, J
dc.date.accessioned2022-06-29T19:42:21Z
dc.date.available2022-06-29T19:42:21Z
dc.date.issued2022
dc.identifier.issn1022-1824
dc.identifier.others00029-022-00780-4
dc.identifier.other780
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338434
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>We use techniques from Gromov–Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane arrangement, our invariants coincide with virtual fundamental classes used to define the logarithmic Gromov–Witten theory of wonderful models of arrangement complements, for any logarithmic structure supported on the wonderful boundary. When the boundary is empty, this implies that the quantum cohomology ring of a hyperplane arrangement’s wonderful model is a combinatorial invariant, i.e., it depends only on the matroid. When the boundary divisor is maximal, we use toric intersection theory to convert the virtual fundamental class into a balanced weighted fan in a vector space, having the expected dimension. We explain how the associated Gromov–Witten theory is completely encoded by intersections with this weighted fan. We include a number of questions whose positive answers would lead to a well-defined Gromov–Witten theory of non-realizable matroids.</jats:p>
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.subject14N35
dc.subject14T20
dc.subject14N20
dc.titleGromov–Witten theory and invariants of matroids
dc.typeArticle
dc.date.updated2022-06-29T19:42:20Z
prism.issueIdentifier4
prism.publicationNameSelecta Mathematica, New Series
prism.volume28
dc.identifier.doi10.17863/CAM.85847
dcterms.dateAccepted2022-05-02
rioxxterms.versionofrecord10.1007/s00029-022-00780-4
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1420-9020
cam.issuedOnline2022-06-18


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