Files in this item
Enumerative geometry of elliptic curves on toric surfaces
Item metadata
dc.contributor.author | Len, Y. | |
dc.contributor.author | Ranganathan, D. | |
dc.date.accessioned | 2020-07-02T12:30:07Z | |
dc.date.available | 2020-07-02T12:30:07Z | |
dc.date.issued | 2018-06 | |
dc.identifier | 268424557 | |
dc.identifier | f252a61f-be25-4d77-ac87-bf7fb1d76ce5 | |
dc.identifier | 85046739902 | |
dc.identifier.citation | Len , 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/s11856-018-1698-9 | en |
dc.identifier.issn | 0021-2172 | |
dc.identifier.other | Bibtex: LR | |
dc.identifier.other | ORCID: /0000-0002-4997-6659/work/75610605 | |
dc.identifier.uri | https://hdl.handle.net/10023/20196 | |
dc.description.abstract | We 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.extent | 565397 | |
dc.language.iso | eng | |
dc.relation.ispartof | Israel Journal of Mathematics | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Enumerative geometry of elliptic curves on toric surfaces | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1007/s11856-018-1698-9 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1510.08556 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.