On rational surfaces I. Irreducible curves of arithmetic genus $0$ or $1$
On rational surfaces I. Irreducible curves of arithmetic genus $0$ or $1$
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在有理曲面上 I. 算术亏格 $0$ 或 $1$ 的不可约曲线
DOI：
10.1215/kjm/1250776405
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发表时间：
1960
影响因子：
0.9
通讯作者：
M. Nagata
中科院分区：
文献类型：
--
作者：
M. Nagata
本文证明了非奇异有理曲面上算术亏格为0或1的不可约曲线的一个基本定理，并给出了该定理在以下方面的应用：（1）不含第一类例外曲线的非奇异有理曲面的分类。(2)有理直纹曲面的分类。(3)Cremona平面变换的因式分解(4)不在任何d-1维射影空间中的d次射影曲面的分类。
We are to prove a fundamental theorem on irreducible curves of arithmetic genus 0 or 1 on a non-singular rational surface and to show applications of the theorem to the followings : (1) The classification of non-singular rational surfaces which have no exceptional curves of the first kind. (2) The classification of rational ruled surfaces. (3) Factorization of Cremona plane transformations. (4) Classification of projective surfaces of degree d which are not in any projective space of dimension d -1 .