Algebraic Deformations of Polarized Varieties
Algebraic Deformations of Polarized Varieties
复制标题
极化簇的代数变形
DOI：
10.1017/s0027763000012733
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发表时间：
1968
影响因子：
0.8
通讯作者：
T. Matsusaka
中科院分区：
文献类型：
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作者：
T. Matsusaka
设V是维数n > 1的射影可嵌入完备非奇异簇。设f是V的射影嵌入，U是非奇异簇，W是非奇异簇，φ是W到U上的态射，使得对U的某点u 0，φ-1（u 0）= f（V）.用∑（V）表示所有这些完全非奇异纤维φ-1（u），u ∈ U的集合，因为我们考虑了所有可能的（f，U，W）。假设我们把∑（V）的成员称为V的（代数）变形，并建议从代数几何的观点来研究∑（V），作为曲线情况的推广。这已经采取了至少在当地的科代拉，斯宾塞，仓西和其他人的情况下，特征0从一个更一般的角度来看复杂的流形（比照。[9][16]中的引用）。
Let V be a projectively embeddable complete non-singular variety of dimension n > 1. Let f be a projective embedding of V, U a non-singular variety, W a non-singular variety and φ a morphism of W onto U such that φ-1(u0) = f(V) for some point u0 of U. Denote by ∑(V) the set of all those complete non-singular fibres φ-1(u), u ∈ U, as we consider all possible (f, U, W). Suppose that we call members of ∑(V) (algebraic) deformations of V and propose to study ∑(V) from the stand point of algebraic geometry, as a generalization of the case of curves. This has been taken up at least locally by Kodaira, Spencer, Kuranishi and others in the case of characteristic 0 from a little more general point of view of complex manifolds (cf. [9] and references given in [16]).