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On subelliptic manifolds

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Abstract

A smooth complex quasi-affine algebraic variety Y is flexible if its special group SAut(Y) of automorphisms (generated by the elements of one-dimensional unipotent subgroups of Aut(Y)) acts transitively on Y, and an algebraic variety is stably flexible if its product with some affine space is flexible. An irreducible algebraic variety X is locally stably flexible if it is a union of a finite number of Zariski open sets each of which is stably flexible. The main result of this paper states that the blowup of a locally stably flexible variety along a smooth algebraic subvariety (not necessarily equidimensional or connected) is subelliptic, and, therefore, it is an Oka manifold.

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Author notes

  1. Tuyen Trung Truong

    Present address: Current address: Department of Mathematics, University of Oslo, Blindern, 0316, Oslo, Norway

Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Shulim Kaliman

  2. Department of Mathematics, University of Bern, Bern, 3012, Switzerland

    Frank Kutzschebauch

  3. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia

    Tuyen Trung Truong

Authors
  1. Shulim Kaliman
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  2. Frank Kutzschebauch
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  3. Tuyen Trung Truong
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Corresponding author

Correspondence to Shulim Kaliman.

Additional information

Dedicated to Mikhail Zaidenberg on the occasion of his 70-th birthday

The second author was partially supported by Schweizerische Nationalfonds grants No. 200020-134876/1 and 200021-140235/1.

The third author was supported by Australian Research Council grants DP120104110 and DP150103442.

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Kaliman, S., Kutzschebauch, F. & Truong, T.T. On subelliptic manifolds. Isr. J. Math. 228, 229–247 (2018). https://doi.org/10.1007/s11856-018-1760-7

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  • DOI: https://doi.org/10.1007/s11856-018-1760-7

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