1, 2, 2, ... and the rest of the points have the generic sequence 1, 1, 1, 2, ... In particular, a genus 2 curve is a hyperelliptic curve. For it is always true that at most points the sequence starts with ones and there are finitely many points with other sequences (see Weierstrass points). Riemann–Roch for line bundles Using the close correspondence between divisors and holomorphic line bundles on a Riemann surface, the theorem can also be stated in a different, yet equivalent way: let L be a holomorphic line bundle on X. Let denote the space of holomorphic sections of L. This space will be finite-dimensional; its dimension is denoted . Let K denote the canonical bundle on X. Then, the Riemann–Roch theorem states that The theorem of the previous section is the special case of when L is a point bundle. The theorem can be applied to show that there are g linearly independent holomorphic sections of K, or one-forms on X, as follows. Taking L to be the trivial bundle, since the only holomorphic functions on X are constants. The degree of L is zero, and is the trivial bundle. Thus, Therefore, , proving that there are g holomorphic one-forms. Degree of canonical bundle Since the canonical bundle has , applying Riemann–Roch to gives which can be rewritten as hence the degree of the canonical bundle is . Riemann–Roch theorem for algebraic curves Every item in the above formulation of the Riemann–Roch theorem for divisors on Riemann surfaces has an analogue in algebraic geometry. The analogue of a Riemann surface is a non-singular algebraic curve C over a field k. The difference in terminology (curve vs. surface) is because the dimension of a Riemann surface as a real manifold is two, but one as a complex manifold. The compactness of a Riemann surface is paralleled by the condition that the algebraic curve be complete, which is equivalent to being projective. Over a general field k, there is no good notion of singular (co)homology. The so-called geometric genus is defined as i.e., as the dimension of the space of globally defined (algebraic) one-forms (see Kähler differential). Finally, meromorphic functions on a Riemann surface are locally represented as fractions of holomorphic functions. Hence they are replaced by rational functions which are locally fractions of regular functions. Thus, writing for the dimension (over k) of the space of rational