Enumerative aspects of the Gross-Siebert program

6533b831fe1ef96bd129876d

RESEARCH PRODUCT

Enumerative aspects of the Gross-Siebert program

Michel Van Garrel D. Peter Overholser Helge Ruddat

subject

Mathematics - Algebraic Geometry FOS: Mathematics Algebraic Geometry (math.AG)Mathematics::Symplectic Geometry Physics::Atmospheric and Oceanic Physics

description

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.

year	journal	country	edition	language
2014-10-17

http://arxiv.org/abs/1410.4783

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