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AFFINE THREEFOLDS WITH \( \mathbb{A} \) 2-FIBRATIONS

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Abstract

An affine threefold containing an \( \mathbb{A} \) 2-cylinder is studied. The existence of \( \mathbb{A} \) 2-cylinders is almost equivalent to the existence of mutually commuting, independent Ga-actions σ1, σ2. A typical example of such affine threefolds is a hypersurface x m y = f(x, z, t), and we generalize such a hypersurface to define an affine pseudo-3-space. After I. Hedén [He], we observe also a Ga-action on the hypersurface x m y = f(x, z, t) with m ≥ 2.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400001, India

    R. V. GURJAR

  2. School of Science & Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, 669-1337, Japan

    K. MASUDA

  3. Research Center for Mathematical Sciences, Kwansei Gakuin University, 2-1 Gakuen, Sanda, 669-1337, Japan

    M. MIYANISHI

Authors
  1. R. V. GURJAR
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  2. K. MASUDA
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  3. M. MIYANISHI
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Correspondence to M. MIYANISHI.

Additional information

(K. MASUDA) Supported by Grant-in-Aid for Scientific Research (C) 22540059, JSPS.

(M. MIYANISHI) Supported by Grant-in-Aid for Scientific Research (B) 24340006, JSPS.

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GURJAR, R.V., MASUDA, K. & MIYANISHI, M. AFFINE THREEFOLDS WITH \( \mathbb{A} \) 2-FIBRATIONS. Transformation Groups 22, 187–205 (2017). https://doi.org/10.1007/s00031-016-9379-4

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  • DOI: https://doi.org/10.1007/s00031-016-9379-4

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