Topics in the Geometry of Projective Space
Topics in the Geometry of Projective Space
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射影空间几何专题
DOI：
10.1007/978-3-0348-9348-0
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
A. V. Ven
中科院分区：
文献类型：
--
作者：
R. Lazarsfeld;A. V. Ven
在DMV研讨会上讨论的主要议题是连通性定理的富尔顿和汉森，线性规范和子品种的小余维投影空间。它们密切相关;因此，连通性定理可以用来证明不等式的一部分，哈茨霍恩猜想的线性正规，而德利涅的推广的连通性定理导致一个完善的巴特的结果拓扑的品种与小余维在一个射影空间。关于连通性定理本身的材料（包括非常令人惊讶的应用到射影平面的tamely分歧覆盖）可以在富尔顿和第一作者W。富尔顿河张文，《代数几何中的连通性及其应用》，《数学讲义》，第862期，第26-92页（Springer 1981）。我从来没有打算把它写在这些笔记里。至于线性正态性，情况就不同了。主要的一点是对扎克工作的阐述，其中大部分都没有参考，但他的信件。因此，把讲座内容的扩展版本作为这些笔记的中心部分是合适的。
The main topics discussed at the DMV Seminar were the connectedness theorems of Fulton and Hansen, linear normality and subvarieties of small codimension in projective spaces. They are closely related; thus the connectedness theorem can be used to prove the inequality-part of Hartshorne's conjecture on linear normality, whereas Deligne's generalisation of the connectedness theorem leads to a refinement of Barth's results on the topology of varieties with small codimension in a projective space. The material concerning the connectedness theorem itself (including the highly surprising application to tamely ramified coverings of the projective plane) can be found in the paper by Fulton and the first author: W. Fulton, R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Lecture Notes in Math. 862, p. 26-92 (Springer 1981). It was never intended to be written out in these notes. As to linear normality, the situation is different. The main point was an exposition of Zak's work, for most of which there is no reference but his letters. Thus it is appropriate to take an extended version of the content of the lectures as the central part of these notes.