Eisenbud's theorem

Eisenbud's theorem describes the structure of minimal free resolutions of certain algebraic objects called complete intersections. In simpler terms, when you study solutions to polynomial equations that form a neat and well-behaved geometric shape, Eisenbud's theorem provides a precise way to understand the relationships among those solutions and their algebraic properties. It shows that these relationships follow a predictable pattern, especially for the complex but well-behaved cases—allowing mathematicians to analyze and compute the structure of these solutions systematically.