On the Orders of the Automorphism Groups of Certain Projective Manifolds
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.
KeywordsAutomorphism Group Abelian Subgroup Isotropy Subgroup Chern Number Base Curve
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- [DK]Deligne, P. and Katz, N., Groupes de Monodromie en Geometrie Algébrique (SGA 7 II), Springer Lecture Notes 370, Springer Verlag, Heidelberg, 1973.Google Scholar
- [S]Shafarevich, I.R., Algebraic Surfaces, Proceedings of the Steklov Institute 75, American Mathematical Society, Providence, 1967.Google Scholar
- [T]Tu, L.W., “Variation of Hodge structure and the local Torelli problem,” Harvard University Thesis, 1979.Google Scholar