# Irregularity

A numerical invariant of a non-singular projective algebraic variety , equal to the dimension of its Picard variety. If the ground field has characteristic zero (or, more general, if the Picard scheme of is reduced), then the irregularity coincides with the dimension of the first cohomology space with coefficients in the structure sheaf.

A variety with non-zero irregularity is called irregular, and a variety with zero irregularity — regular. Sometimes the -th irregularity of a complete linear system on a variety is defined as

where .