Brief introduction to tropical geometry
Erwan Brugall\'e, Ilia Itenberg, Grigory Mikhalkin, Kristin Shaw
TL;DR
This paper provides an accessible introduction to tropical geometry, covering tropical curves, their applications in enumerative geometry, and general tropical varieties with homology theories, based on lecture notes from a conference mini-course.
Contribution
It offers a comprehensive, beginner-friendly overview of tropical geometry concepts, applications, and advanced topics not widely covered in existing literature.
Findings
Tropical curves can be used to solve classical enumerative geometry problems.
The paper introduces homology theories for tropical varieties.
It bridges tropical geometry with traditional algebraic geometry applications.
Abstract
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.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications