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Nonabelian holomorphic Lie algebroid extensions. (English) Zbl 1317.32036

Summary: We classify nonabelian extensions of Lie algebroids in the holomorphic category. Moreover we study a spectral sequence associated to any such extension. This spectral sequence generalizes the Hochschild-Serre spectral sequence for Lie algebras to the holomorphic Lie algebroid setting. As an application, we show that the hypercohomology of the Atiyah algebroid of a line bundle has a natural Hodge structure.

MSC:

32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
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[1] Abad C. A., J. Reine Angew. Math. 663 pp 91– (2012)
[2] A. BeĬlinson and J. Bernstein, I. M. Gel’fand Seminar, Advances in Soviet Mathematics 16 (American Mathematical Society, Providence, RI, 1993) pp. 1–50.
[3] DOI: 10.1016/j.geomphys.2009.10.006 · Zbl 1207.58018 · doi:10.1016/j.geomphys.2009.10.006
[4] DOI: 10.1007/978-0-8176-4745-2_4 · Zbl 1230.14010 · doi:10.1007/978-0-8176-4745-2_4
[5] DOI: 10.1007/s11232-010-0132-1 · Zbl 1252.32034 · doi:10.1007/s11232-010-0132-1
[6] DOI: 10.2307/1969215 · Zbl 0029.34001 · doi:10.2307/1969215
[7] DOI: 10.2307/1969174 · Zbl 0029.34101 · doi:10.2307/1969174
[8] Grothendieck A., Publ. Math. Inst. Hautes Études Sci. 11 pp 1– (1961)
[9] DOI: 10.2307/2372650 · Zbl 0057.27204 · doi:10.2307/2372650
[10] DOI: 10.2307/1969740 · Zbl 0053.01402 · doi:10.2307/1969740
[11] DOI: 10.1090/conm/227/03255 · doi:10.1090/conm/227/03255
[12] Katz N., J. Math. Kyoto Univ. 8 pp 198– (1968)
[13] Laurent-Gengoux C., Int. Math. Res. Not. 2008 pp 46– (2008)
[14] DOI: 10.1215/S0012-7094-97-08608-7 · Zbl 0889.58036 · doi:10.1215/S0012-7094-97-08608-7
[15] DOI: 10.1017/CBO9781107325883 · doi:10.1017/CBO9781107325883
[16] DOI: 10.1017/S0017089500032055 · Zbl 0886.22012 · doi:10.1017/S0017089500032055
[17] DOI: 10.2969/jmsj/00520171 · Zbl 0051.02304 · doi:10.2969/jmsj/00520171
[18] DOI: 10.1090/S0002-9947-1963-0154906-3 · doi:10.1090/S0002-9947-1963-0154906-3
[19] DOI: 10.1070/RM1980v035n04ABEH001882 · Zbl 0465.58029 · doi:10.1070/RM1980v035n04ABEH001882
[20] DOI: 10.1007/BF02950735 · doi:10.1007/BF02950735
[21] DOI: 10.1007/BF01694897 · JFM 52.0113.04 · doi:10.1007/BF01694897
[22] DOI: 10.2969/jmsj/01830275 · Zbl 0144.27201 · doi:10.2969/jmsj/01830275
[23] DOI: 10.1017/CBO9780511661761 · doi:10.1017/CBO9780511661761
[24] DOI: 10.2478/s11533-012-0065-z · Zbl 1279.14016 · doi:10.2478/s11533-012-0065-z
[25] Voisin C., Cambridge Studies in Advanced Mathematics 76, in: Hodge Theory and Complex Algebraic Geometry. I (2007)
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