In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves.
Furthermore, it has applications to the theory of modular forms on reductive algebraic groups[1] and string theory.
is the space of holomorphic differentials on the curve C. To define the Hodge bundle, let
be the universal algebraic curve of genus g and let
The Hodge bundle is the pushforward of this sheaf, i.e.,[3]