Abstract
In [13] the author gives a geometric construction of the indicator set of Sherk associated to a finite spread. In this paper we construct the indicator set in the general case (finite and not finite) and we characterize an indicator set associated to a pappian spread. Between this indicator set we can determinate the representation of a spread of Galois on the Grassmann variety.
Similar content being viewed by others
Bibliografia
Biliotti, M. and Lunardon, G.: ‘Insiemi di derivazione e sottopiani di Baer in un piano di translazione’. Rend. Acc. Naz. Lincei 69 (1980), 135–141.
Burau, W.: Mehrdimensonale projective und höhere Geometrie. Berlin, 1961.
Dembowski, P.: Finite Geometries. Springer-Verlag, 1968.
Greub, W.: Multilinear Algebra. Springer-Verlag, 1967.
Grundhöfer, T.: ‘Eine Charakterisierung ableitbarer Translationsebenen’. Geom. Dedicata 11 (1981), 177–185.
Herzer, A.: ‘Lineare Kongruenzen, die aus freien zyklischen Moduln halbeinfacher Algebren bestehen’. Arch. Math. 30 (1978), 14–26.
Herzer, A.: ‘Die Schmieghyperebenen an die Mannigfaltigkeit von Veronese bei beliebiger Charakteristik’. J. Geometry 18 (1982), 140–154.
Herzer, A.: ‘Varietà di Segre generalizzate’ (in corso di stampa).
Hodge, W. V. D. and Pedoe, D.: Methods of Algebraic Geometry: I, II. University Press. Cambridge, 1947.
Hughes, D. R. and Piper, F. C.: Projective Planes. Springer-Verlag, 1972.
Limbos, M.: ‘A Characterisation of the Embeddings of PG(m, q) into PG(n, q h)’. J. Geometry 16 (1981), 50–55.
Lunardon, G.: ‘Piani di translazione derivabili’. Rend. Sem. Mat. Univ. Padova 61 (1979), 271–284.
Lunardon, G.: ‘Insiemi indicatori proiettivi e fibrazioni planari di uno spazio proiettivo finito’ (in corso di stampa sul Boll. U.M.I.).
Lüneburg, H.: Translation Planes. Springer-Verlag, 1980.
Morin, U.: ‘Contributi alla geometria degli S k di S n ’. Rend Sem. Mat. Univ. Padova 3 (1932), 82–94.
Shafarevich, I. R.: Basic Algebraic Geometry. Springer-Verlag, 1974.
Sherk, F. A.: ‘Indicator Set in an Affine Space of Any Dimension’. Can. J. Math. 31 (1979), 211–224.
Author information
Authors and Affiliations
Additional information
Lavoro eseguito nell'ambito delle attività del-G.N.S.A.G.A. del C.N.R.
Rights and permissions
About this article
Cite this article
Lunardon, G. Fibrazioni planari e sottovarietà algebriche della varietà di Grassmann. Geom Dedicata 16, 291–313 (1984). https://doi.org/10.1007/BF00147873
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00147873