Abstract
The automorphisms of line congruences in ℙ3 are studied via the analysis of the automorphisms of the associated focal loci. This study is applied to a Veronese surface (i.e. to a congruence of chords of a twisted cubic) and to the rational scrolls in the Grassmannian G(1, 3).
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References
Cossec, F., Dolgachev, I. and Verra, A. (in preparation).
Goldstein, N., ‘A Special Surface in the 4-Quadric’, Duke Math. J. 50 (1983), 745–761.
Goldstein, N., ‘Examples of Non-ample Normal Bundles’, Composition Math. 51 (1984), 189–192.
Goldstein, N., ‘The Geometry of Surfaces in the 4-Quadric’, Preprint, 1985.
Goldstein, N., ‘Scroll Surfaces in G(1, ℙ3)’, Preprint, 1985.
Jessop, C., A Treatise on the Line Complex, Cambridge Univ. Press, 1903.
Matsumura, H. and Monsky, P., ‘On the Automorphisms of Hypersurfaces’, J. Math. Kyoto Univ. 3 (1964), 347–361.
Papantonopoulou, A., ‘Embeddings in G(1, 3)’, Proc. Amer. Math. Soc. 89 (1983), 583–586.
Papantonopoulou, A., ‘Embeddings of Geometrically Ruled Surfaces in the 4-Quadric’, Canad. Math. Soc. Conference Proc., No. 6, 1986, pp. 365–367.
Papantonopoulou, A., ‘Minimal Surfaces in the 4-Quadric’, Bull. Greek Math. Soc. 25 (1984), 107–112.
Ran, Z., ‘Surfaces of Order 1 in Grassmannians’, J. reine angew. Math. 368 (1986), 119–126.
Semple, J. G. and Roth, L., Introduction to Algebraic Geometry, Oxford Univ. Press, 1949.
Turrini, C., ‘Gli automorfismi delle rigate geometriche razionali’, Istituto Lombardo (Rend. Sc.) A113 (1979), 210–223.
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Bertolini, M., Turrini, C. On the automorphisms of some line congruences in ℙ3 . Geom Dedicata 27, 191–197 (1988). https://doi.org/10.1007/BF00151349
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DOI: https://doi.org/10.1007/BF00151349