Classification of compact complex homogeneous spaces with invariant volumes
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Abstract:
We solve the problem of the classification of compact complex homogeneous spaces with invariant volumes (see Matsushima, 1961).References
- J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
- D. N. Akhiezer: A Bound for the Dimension of the Automorphism Group of a Compact Complex Homogeneous Space. Soobshch. Akad. Nauk. Grus. SSR (Russian) 110 (1983), 469–472.
- D. N. Akhiezer: Homogeneous Complex Manifolds, in Several Complex Variables IV, Encyclopaedia of Math. Sci., vol. 10, (1994), 195–244.
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145 (1961/62), 429–439 (German). MR 145557, DOI 10.1007/BF01471087
- Josef Dorfmeister and Zhuang Dan Guan, Classification of compact homogeneous pseudo-Kähler manifolds, Comment. Math. Helv. 67 (1992), no. 4, 499–513. MR 1185806, DOI 10.1007/BF02566516
- Josef Dorfmeister and Zhuang Dan Guan, Fine structure of reductive pseudo-Kählerian spaces, Geom. Dedicata 39 (1991), no. 3, 321–338. MR 1123147, DOI 10.1007/BF00150759
- Josef Dorfmeister and Zhuang Dan Guan, Pseudo-Kählerian homogeneous spaces admitting a reductive transitive group of automorphisms, Math. Z. 209 (1992), no. 1, 89–100. MR 1143216, DOI 10.1007/BF02570823
- Josef Dorfmeister and Kazufumi Nakajima, The fundamental conjecture for homogeneous Kähler manifolds, Acta Math. 161 (1988), no. 1-2, 23–70. MR 962095, DOI 10.1007/BF02392294
- H. Grauert and R. Remmert, Über kompakte homogene komplexe Mannigfaltigkeiten, Arch. Math. (Basel) 13 (1962), 498–507 (German). MR 145558, DOI 10.1007/BF01650099
- Daniel Guan, Examples of compact holomorphic symplectic manifolds which admit no Kähler structure, Geometry and analysis on complex manifolds, World Sci. Publ., River Edge, NJ, 1994, pp. 63–74. MR 1463964
- Daniel Guan, A splitting theorem for compact complex homogeneous spaces with a symplectic structure, Geom. Dedicata 63 (1996), no. 2, 217–225. MR 1413633, DOI 10.1007/BF00148221
- Daniel Guan, Classification of compact homogeneous spaces with invariant symplectic structures, Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 52–54. MR 1464575, DOI 10.1090/S1079-6762-97-00023-1
- D. Guan: Toward a Classification of Complex Homogeneous Spaces, preprint, 1998.
- Daniel Guan, Classification of compact complex homogeneous spaces with invariant volumes, Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 90–92. MR 1465831, DOI 10.1090/S1079-6762-97-00028-0
- Jun-ichi Hano, Equivariant projective immersion of a complex coset space with non-degenerate canonical hermitian form, Scripta Math. 29 (1973), 125–139. MR 367315
- Jun-ichi Hano, On compact complex coset spaces of reductive Lie groups, Proc. Amer. Math. Soc. 15 (1964), 159–163. MR 158030, DOI 10.1090/S0002-9939-1964-0158030-1
- G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
- A. T. Huckleberry, Homogeneous pseudo-Kählerian manifolds: a Hamiltonian viewpoint, Note Mat. 10 (1990), no. suppl. 2, 337–342. MR 1221949
- Jun-ichi Hano and Shoshichi Kobayashi, A fibering of a class of homogeneous complex manifolds, Trans. Amer. Math. Soc. 94 (1960), 233–243. MR 115188, DOI 10.1090/S0002-9947-1960-0115188-9
- A. Huckleberry and E. Oeljeklaus, Classification theorems for almost homogeneous spaces, Institut Élie Cartan, vol. 9, Université de Nancy, Institut Élie Cartan, Nancy, 1984. MR 782881
- James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
- Takashi Iwamoto, Density properties of complex Lie groups, Osaka J. Math. 23 (1986), no. 4, 859–865. MR 873214
- Takashi Iwamoto, Algebraic groups and co-compact subgroups of complex linear groups, Mem. Fac. Sci. Kyushu Univ. Ser. A 42 (1988), no. 1, 1–7. MR 937000, DOI 10.2206/kyushumfs.42.1
- Shoshichi Kobayashi, Differential geometry of complex vector bundles, Publications of the Mathematical Society of Japan, vol. 15, Princeton University Press, Princeton, NJ; Princeton University Press, Princeton, NJ, 1987. Kanô Memorial Lectures, 5. MR 909698, DOI 10.1515/9781400858682
- R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749. MR 242166, DOI 10.1090/S0002-9904-1969-12271-8
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Yozô Matsushima, Sur certaines variétés homogènes complexes, Nagoya Math. J. 18 (1961), 1–12 (French). MR 138704, DOI 10.1017/S0027763000002191
- M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, 1972. MR 0507234, DOI 10.1007/978-3-642-86426-1
- Atle Selberg, On discontinuous groups in higher-dimensional symmetric spaces, Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960) Tata Institute of Fundamental Research, Bombay, 1960, pp. 147–164. MR 0130324
- J. Tits, Espaces homogènes complexes compacts, Comment. Math. Helv. 37 (1962/63), 111–120 (French). MR 154299, DOI 10.1007/BF02566965
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
- Jörg Winkelmann, Complex analytic geometry of complex parallelizable manifolds, Mém. Soc. Math. Fr. (N.S.) 72-73 (1998), x+219 (English, with English and French summaries). MR 1654465
Additional Information
- Daniel Guan
- Affiliation: Department of Mathematics, The University of California at Riverside, Riverside, California 92521
- Email: zguan@math.ucr.edu
- Received by editor(s): September 28, 2001
- Received by editor(s) in revised form: April 21, 2002
- Published electronically: July 2, 2002
- Additional Notes: Supported by NSF Grants DMS-9401755 and DMS-9627434
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 4493-4504
- MSC (2000): Primary 53C30, 32M10, 32M05, 14M17; Secondary 14M20, 53C10, 53C56
- DOI: https://doi.org/10.1090/S0002-9947-02-03102-1
- MathSciNet review: 1926885