The Canonical Ring of an Algebraic Surface by David Mumford
نویسنده
چکیده
B7t nC + Bv(n) where v(n) is one of the integers 1, 2, • • • , m (Theorem 8.1; Theorem 10.1; Theorem 11.4). Thus, under the assumption that dim I hD I > 0 for some h, B„ is bounded (from above) if and only if D is arithmetically effective.' (7) If the quadratic form (pi, is of type (0, t), the function v(n) which occurs in (6) is periodic (Theorem 11.4). (8) The ring KID] (introduced in § 2) is finitely generated over k if and only if one of the following conditions is satisfied: (8a) q is of type (1, t) and some multiple I h(D — (6 " = arithmetically negative component of D) has no fixed components; (8b) (pi, is of type (0, t) (Theorem 10.6; Proposition 11.5). In the case (8b), RID] has transcendence degree < 1 over k.
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