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Holomorphic \(\text {GL}_2({\mathbb C})\)-geometry on compact complex manifolds


We study holomorphic \(\text {GL}_2({\mathbb {C}})\) and \(\text {SL}_2({\mathbb C})\) geometries on compact complex manifolds.

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The authors would like to thank Charles Boubel who kindly explained the geometric construction of the noncompact dual \(D_3\) of the quadric \(Q_3\) presented in Sect. 2. The authors wish to thank the referee for very careful reading of the manuscript and helpful comments. This work has been supported by the French government through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR2152IDEX201. The first-named author is partially supported by a J. C. Bose Fellowship, and school of mathematics, TIFR, is supported by 12-R & D-TFR-5.01-0500. The second-named author wishes to thank TIFR Mumbai, ICTS Bangalore and IISc Bangalore for hospitality.

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Correspondence to Sorin Dumitrescu.

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Biswas, I., Dumitrescu, S. Holomorphic \(\text {GL}_2({\mathbb C})\)-geometry on compact complex manifolds . manuscripta math. 166, 251–269 (2021).

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Mathematics Subject Classification

  • 53C07
  • 53C10
  • 32Q57