On the Orders of the Automorphism Groups of Certain Projective Manifolds
On the Orders of the Automorphism Groups of Certain Projective Manifolds
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某些射影流形的自同构群的阶
DOI：
10.1007/978-1-4612-5987-9_7
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
A. Sommese
中科院分区：
文献类型：
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作者：
A. Howard;A. Sommese
Hurwitz的一个著名定理是亏格g > 1的紧致Riemann曲面的自同构群的阶不大于84（g - 1）。Bochner和小林分别证明了具有负Ricci张量的紧致黎曼流形具有有限自同构群和具有负第一Chern类的紧致复流形具有相同的结论[K]。Matsumura [M1]研究了双有理变换群，证明了它不包含单参数子群，只要流形有充足的标准丛。
It is a well-known theorem of Hurwitz that the automorphism group of a compact Riemann surface of genus g > 1 has order not larger than 84 (g - 1). This was generalized by Bochner who proved that a compact Riemannian manifold with negative Ricci tensor has a finite automorphism group, and Kobayashi who derived the same conclusion for a compact complex manifold with negative first Chern class [K]. The group of birational transformations was studied by Matsumura [M1] who proved that it contains no one-parameter subgroup, provided the manifold has ample canonical bundle.