Non-general Type Surfaces in P4: Some Remarks on Bounds and Constructions
Non-general Type Surfaces in P4: Some Remarks on Bounds and Constructions
复制标题
P4 中的非一般类型表面：关于边界和构造的一些评论
DOI：
10.1006/jsco.1999.0323
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
F. Schreyer
中科院分区：
文献类型：
--
作者：
W. Decker;F. Schreyer
布赫伯格算法在现代计算机代数系统中的快速实现允许计算代数几何中的复杂示例。在过去几年中，此类计算有助于预测和检验代数几何中的许多定理。反之亦然，受到代数几何复杂例子的启发，计算机代数开发人员改进了他们的算法和实现。在本文中，我们介绍了计算机代数在射影代数几何中的一些典型应用。我们关注一个具体问题，即P4中非通用类型曲面的分类。我们首先来介绍一下这个问题。如果 S⊂ Pn，n≥ 6，是一个光滑表面，那么它的割线变化 Sec(S) 不会填满 Pn，我们可以通过从 Sec(S) 上一点的线性投影将 S 嵌入到 Pn−1 中。然而，对于 n= 5，由于以下经典定理，情况有所不同。
The fast implementation of Buchberger’s algorithm in modern computer algebra systems allows the computation of complicated examples in algebraic geometry. During the last couple of years such computations have helped to predict and check many theorems in algebraic geometry. Vice versa, inspired by complicated examples coming from algebraic geometry, computer algebra developers have refined their algorithms and implementations. In this paper we present some typical applications of computer algebra to projective algebraic geometry. We focus on one specific problem, namely the classification of non-general type surfaces in P4. Let us start with an introduction to this problem. If S⊂ Pn, n≥ 6, is a smooth surface, then its secant variety Sec (S) does not fill up Pn, and we may embed S into Pn− 1 via a linear projection from a point off Sec (S). For n= 5, however, the situation is different due to the following classical theorem.