In mathematics, a Prym differential of a

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

is a

differential form In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, ...

on the universal covering space that transforms according to some complex

character Character or Characters may refer to: Arts, entertainment, and media Literature * ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk * ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...

of the

fundamental group In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...

. Equivalently it is a section of a certain line bundle on the

in the same component as the canonical bundle. Prym differentials were introduced by . The space of Prym differentials on a compact Riemann surface of genus ''g'' has dimension ''g'' – 1, unless the character of the fundamental group is trivial, in which case Prym differentials are the same as ordinary differentials and form a space of dimension ''g''.

References

* * Riemann surfaces {{Riemannian-geometry-stub