Clifford's theorem on special divisors

In mathematics, Clifford's theorem on special divisors is a result of on algebraic curves, showing the constraints on special linear systems on a curve C. Statement A divisor on a Riemann surface C is a formal sum of points P on C with integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining as the vector space of functions having poles only at points of D with positive coefficient, at most as bad as the coefficient indicates, and having zeros at points of D with negative coefficient, with at least that multiplicity. The dimension of is finite, and denoted . The linear system of divisors attached to D is the corresponding projective space of dimension . The other significant invariant of D is its degree d, which is the sum of all its coefficients. A divisor is called special if ℓ(K − D) > 0, where K is the canonical divisor.