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dc.contributor.authorLen, Y.
dc.contributor.authorRanganathan, D.
dc.date.accessioned2020-07-02T12:30:07Z
dc.date.available2020-07-02T12:30:07Z
dc.date.issued2018-06
dc.identifier.citationLen , Y & Ranganathan , D 2018 , ' Enumerative geometry of elliptic curves on toric surfaces ' , Israel Journal of Mathematics , vol. 226 , pp. 351–385 . https://doi.org/10.1007/s11856-018-1698-9en
dc.identifier.issn0021-2172
dc.identifier.otherPURE: 268424557
dc.identifier.otherPURE UUID: f252a61f-be25-4d77-ac87-bf7fb1d76ce5
dc.identifier.otherBibtex: LR
dc.identifier.otherScopus: 85046739902
dc.identifier.otherORCID: /0000-0002-4997-6659/work/75610605
dc.identifier.urihttps://hdl.handle.net/10023/20196
dc.description.abstractWe establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed j-invariant, refining results of Mikhalkin and Nishinou--Siebert. As an application, we determine a formula for such counts on ℙ2 and all Hirzebruch surfaces. This formula relates the count of elliptic curves with the number of rational curves on the surface satisfying a small number of tangency conditions with the toric boundary. Furthermore, the combinatorial tropical multiplicities of Kerber and Markwig for counts in ℙ2 are derived and explained algebro-geometrically, using Berkovich geometry and logarithmic Gromov--Witten theory. As a consequence, a new proof of Pandharipande's formula for counts of elliptic curves in ℙ2 with fixed j-invariant is obtained.
dc.language.isoeng
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.rightsCopyright © 2018, The Hebrew University of Jerusalem. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s11856-018-1698-9en
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleEnumerative geometry of elliptic curves on toric surfacesen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s11856-018-1698-9
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1510.08556en


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