Chow ring
One of the advantages of the Grothendieck–Riemann–Roch formula is it can be interpreted as a relative version of the Hirzebruch–Riemann–Roch formula. For example, a smooth morphism formula_28 has fibers which are all equi-dimensional (and isomorphic as topological spaces when base changing to formula_29). This fact is useful in moduli-theory when considering a moduli space formula_30 parameterizing smooth proper spaces. For example, David Mumford used this formula to deduce relationships of the Chow ring on the moduli space of algebraic curves.