1962/11/01 by Oscar Zariski · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Mathematics #Divisor (algebraic geometry) #Algebraic surface #Algebraic number #Pure mathematics #Irreducible component #Algebraic cycle #Ring (chemistry) #Base (topology) #Algebra over a field #Mathematical analysis
paper · doi:10.2307/1970376
openalex publication_date 1962/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/23
Part I. The problem and its background ? 1. Formulation of the problem ? 2. A ring-theoretic aspect of the problem ? 3. Connection with the generalized 14th problem of Hilbert Part II. Preliminary results on linear systems free from base points ? 4. On certain graded subrings in function fields ? 5. On certain graded R*-modules defined by linear systems ? 6. Applications to non-singular algebraic surfaces Part III. Solution of the general problem ? 7. The arithmetically negative component of an effective cycle D ? 8. Reduction to the case of arithmetically effective cycles ? 9. A theorem on arithmetically effective cycles ?10. Boundedness of the superabundance and of the fixed component of InDI (D arithmetically effective, (D of type (1, t)) ?11. The case D?O< ? ?12. A summary of principal results APPENDIX. The canonical ring of an algebraic surface. By DAVID MUMFORD.