Enumerative tropical algebraic geometry in R2

Simple item page
dc.creatorMikhalkin, Grigory
dc.date2003-12-31
dc.date2004-12-05
dc.date.accessioned2026-07-07T05:04:19Z
dc.date.available2026-07-07T05:04:19Z
dc.descriptionThe paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in the Newton polygon. The formula was announced earlier in http://arxiv.org/abs/math.AG/0209253. The result is established with the help of the so-called tropical algebraic geometry. This geometry allows one to replace complex toric varieties with the Euclidean n-space and holomorphic curves with certain piecewise-linear graphs there.
dc.description83 pages, 20 figures, Version 4, to appear in the Journal of the AMS
dc.identifierhttps://arxiv.org/abs/math/0312530
dc.identifierhttp://arxiv.org/abs/math/0312530
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69760
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.titleEnumerative tropical algebraic geometry in R2
dc.typetext

Files

Collections

arXiv