Introduction to Tropical Algebraic Geometry
đź“ś Abstract
This paper is an invitation to the combinatorial, geometric, and algorithmic aspects of tropical algebraic geometry. It is written for beginning graduate students and researchers who work either in combinatorics or in algebraic geometry. We start out with a self-contained introduction to tropical geometry, including the requisite background from polyhedral geometry, and then proceed to the main research topics in this field. We emphasize that tropical algebraic geometry is an increasingly active subject which is ripe for further development and has many applications to other areas of mathematics.
✨ Summary
The paper “Introduction to Tropical Algebraic Geometry” by Diane Maclagan and Bernd Sturmfels serves as an introductory guide to the field of tropical algebraic geometry, intended for graduate students and researchers with backgrounds in combinatorics or algebraic geometry. It provides a self-contained overview of tropical geometry concepts and connections with polyhedral geometry and discusses key research topics in the domain. \n\nThe paper is a foundational document for those new to the subject, offering both theoretical insights and algorithmic approaches. Tropical algebraic geometry is highlighted as an evolving field with emerging applications across various mathematical disciplines. \n\nDespite being written in 2004, the paper has continued to influence research by promoting further exploration in tropical mathematics. However, direct citations or significant industrial applications of this specific work are scarce in current academic literature, reflecting the paper’s primary role in education and theoretical introduction, rather than industrial innovation.