Applications of Algebraic Geometry in Contemporary Physics

Abstract

Algebraic geometry, a branch of mathematics that studies solutions to polynomial equations, has found profound applications in physics, particularly in the context of addressing singularities with significant physical implications. This article delves into the role of algebraic geometry in various areas of physics, including string theory, mirror symmetry, solitons, instanton moduli spaces, and the simplification of computational tasks such as Feynman integral reduction and multi-variable global residue computation. These applications highlight the indispensable contributions of algebraic geometry to the advancement of our understanding of the physical universe.