Hodge bundle
From Wikipedia, the free encyclopedia
From Wikipedia, the free encyclopedia
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.[2]
Let be the moduli space of algebraic curves of genus g curves over some scheme. The Hodge bundle is a vector bundle[note 1] on whose fiber at a point C in 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 be its relative dualizing sheaf. The Hodge bundle is the pushforward of this sheaf, i.e.,[3]
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.