Brief introduction to tropical geometry

By Erwan Brugallé, I. Itenberg, G. Mikhalkin, Kristin M. Shaw. 2015

101 citations recorded by the source corpus.

The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in classical enumerative geometry, and continue with a look at more general tropical varieties and their homology theories.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cfa6473f59f3dc3a4460bc151d774d8e4100156d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Jascha Smacka
2. Kristin M. Shaw
3. Philipp Jell

In Computational Theory and Mathematics

1. Jascha Smacka
2. Kristin M. Shaw
3. Philipp Jell

In Geometry and Topology

1. Jascha Smacka
2. Kristin M. Shaw
3. Philipp Jell

Citations in the corpus

• Superforms, tropical cohomology, and Poincaré duality (2015, methodology): “ity. We begin by showing that matroidal fans in Rr have Poincaré duality. To do this we use an alternative recursive description of matroidal fans via an operation known as tropical modifications (see [BIMS15] for an introduction). In the language of matroids, the operation of tropical modification is”