Irregularity of a surface
In mathematics, the irregularity of a complex surface X is the Hodge number h= dim H(OX), usually denoted by q (Wolf P.Barth,Klaus Hulek&Chris A.M. Peterset al. 2004). The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety (Bombieri & Mumford 1977, p.26), which is the same in characteristic 0 but can be smaller in positive characteristic.