Intersection theory

Summary

Intersection theory studies how subvarieties of an algebraic variety meet, and assigns numbers and classes to their intersections. Its central object is the Chow ring of a smooth variety, made of the Chow groups. Its product sends two cycle classes to the class of their intersection, counted with intersection multiplicity. It gives a rigorous form to classical enumerative geometry, including Bézout's theorem and Schubert calculus. It is also the home of Chern classes and of the Hirzebruch–Riemann–Roch theorem.