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Mathematics > Algebraic Geometry

arXiv:1410.4783 (math)
[Submitted on 17 Oct 2014]

Title:Enumerative aspects of the Gross-Siebert program

Authors:Michel van Garrel, D. Peter Overholser, Helge Ruddat
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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.
Comments: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 pages
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1410.4783 [math.AG]
  (or arXiv:1410.4783v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1410.4783

Submission history

From: D. Peter Overholser [view email]
[v1] Fri, 17 Oct 2014 16:09:39 UTC (2,409 KB)
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