Introduction to Toric Geometry
Simon Telen
TL;DR
This paper provides an introduction to toric geometry, covering affine and projective varieties, divisors, and Cox's construction, with computational examples using Julia's Oscar.jl package.
Contribution
It offers a comprehensive overview of toric varieties, emphasizing computational methods and applications in solving polynomial systems.
Findings
Illustrates the use of Julia's Oscar.jl for computations
Explains Cox's construction as a GIT quotient
Highlights applications in solving polynomial equations
Abstract
These notes are based on a series of lectures given by the author at the Max Planck Institute for Mathematics in the Sciences in Leipzig. Addressed topics include affine and projective toric varieties, abstract normal toric varieties from fans, divisors on toric varieties and Cox's construction of a toric variety as a GIT quotient. We emphasize the role of toric varieties in solving systems of polynomial equations and provide many computational examples using the Julia package Oscar.jl.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications