Curve enumeration and the quintic threefold using tropical methods.

摘要

The Gross-Siebert program provides an algebro-geometrization of the SYZ conjecture; on one side we have toric degenerations and on the other we have a triple (B, P , ϕ) which is an affine manifold with singularities along with some additional data. An integral part of the program is converting the triple (B, P , ϕ) to a toric degeneration. In this paper we will apply the Gross-Siebert program to the quintic threefold up to order two; from this we will perform a period calculation and obtain predictions for the number of lines and conics.