Show simple item record

Files in this item

Thumbnail

Item metadata

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.identifier268424557
dc.identifierf252a61f-be25-4d77-ac87-bf7fb1d76ce5
dc.identifier85046739902
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.otherBibtex: LR
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.format.extent565397
dc.language.isoeng
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleEnumerative geometry of elliptic curves on toric surfacesen
dc.typeJournal articleen
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


This item appears in the following Collection(s)

Show simple item record