The topological type of nonsingular surfaces in RP3 of degree four
The topological type of nonsingular surfaces in RP3 of degree four
复制标题
四阶RP3中非奇曲面的拓扑类型
DOI：
10.1007/bf01076029
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发表时间：
1976
影响因子：
0.4
通讯作者：
V. Kharlamov
中科院分区：
文献类型：
--
作者：
V. Kharlamov
本文证明了在RP 3中存在具有类型（i）和（2）的四次曲面;在证明这一事实时，主要利用了GN Tyurina在她关于K3-曲面的论文中所应用的方法（见[3]，Chap.（IX））。此外，我们可以推导出一个类似的不平等估计由于六阿尔诺！本文证明了在RP的四次曲面中不存在具有（3）~本文的方法还可以用来重新证明RP 3中许多已知的四次曲面拓扑类型的存在性，特别是，我们可以用这种方法得到所有已知的类型，其中//.（P Z2）;~ 20[即，dim H，（P; Za）= 24，22];然而，迄今为止，我们还没有成功地以这种方式穷尽所有已知的类型，我们将自己限制在表面（I）和（2）。
In this paper it is proved that in RP 3 there exist surfaces of degree four having types (i) and (2); in proving this fact, essential use is made of methods applied by GN Tyurina in her paper on K3-surfaces (see [3, Chap. IX]). Furthermore, we can deduce from an inquality analogous to an estimate due to VI Arno!'d for the number of nonempty even ovals of a plane curve, that there do not exist in RP s surfaces of degree four having the type (3)..~ nus, the question formulated above is completely answered.The methods of the present paper can also be used to reprove the existence of many of th already known topological types of surface of degree four in RP 3, in particular, we can obtain in this way all the known types for which//.(P Z2);~ 20[ie, dim H,(P; Za)= 24, 22]; however, we have so far not succeeded in exhausting all the known types in this way, and we restrict ourselves to the surfaces (I) and (2).