The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface
The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface
复制标题
代数曲面上有效除数的高倍数黎曼-罗赫定理
DOI：
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发表时间：
1962
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通讯作者：
O. Zariski
中科院分区：
文献类型：
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作者：
O. Zariski
第一部分.问题及其背景？1.问题的表述？2.这个问题的一个环理论方面？3.与广义希尔伯特第14问题的联系第二部分。关于无基点线性系统的初步结果？4.关于函数域中某些分次子环？5.关于由线性系统定义的某些分次R*-模6.应用于非奇异代数曲面第三部分。解决一般问题？7.有效周期D的算术负分量？8.还原到算术有效周期的情况？9.关于算术有效圈的一个定理？10.有界性的过剩和固定的组成部分的InDI（D算术有效，（D的类型（1，t））？11.案件D？O<？? 12.主要结果摘要附录。代数曲面的标准环。大卫·芒福德。
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.