English

Enumerative aspects of the Gross-Siebert program

Algebraic Geometry 2014-10-20 v1

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.

Cite

@article{arxiv.1410.4783,
  title  = {Enumerative aspects of the Gross-Siebert program},
  author = {Michel van Garrel and D. Peter Overholser and Helge Ruddat},
  journal= {arXiv preprint arXiv:1410.4783},
  year   = {2014}
}

Comments

A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 pages

R2 v1 2026-06-22T06:27:28.231Z