Counting curves via lattice paths in polygons

Details Counting curves via lattice paths in polygons Counting curves via lattice paths in polygons

2002-09-19

arxiv.org/abs/math/0209253v4

Mathematics

Algebraic Geometry

The version to appear as the English part of a paper in C. R. Acad. Sci. Paris

Scientific paper

This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of generic points in the surface. The answer is given in terms of certain lattice paths in the relevant Newton polygon. If the toric surface is the projective plane or the product of two projective lines then the invariants under consideration coincide with the Gromov-Witten invariants. The formula gives a new count even in these cases, where other computational technique is available.

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