Enumerative aspects of the Gross-Siebert program
arXiv:1410.4783
Abstract
We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.
A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 pages