2012/06/09 by Florian Block, Block, Florian
Mathematics · #14N10 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary: 14N35. Secondary: 14T05 #math.AG #math.CO #msc:14N10 #msc:14N35. #msc:14T05
paper · pdf · doi:10.48550/arxiv.1206.1925
14 pages, 6 figures. To appear in Contemporary Mathematics (Proceedings), "Tropical Geometry and Integrable Systems", Glasgow, July 2011
arxiv created 2012/06/09 · arxiv updated 2012/06/12
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to significant progress. In this survey, we give an introduction to tropical geometry techniques for algebraic curve counting problems. We also survey some recent developments, with a particular emphasis on the computation of the degree of the Severi varieties of the complex projective plane and other toric surfaces as well as Hurwitz numbers and applications to real enumerative geometry. This paper is based on the author's lecture at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 2011.