The separability of the Gauss map and the reflexivity for a projective surface

Satoru Fukasawa, Hajime Kaji

    Research output: Contribution to journal › Article

    6 Citations (Scopus)

    Abstract

    It is known that if a projective variety X in P N is reflexive with respect to the projective dual, then the Gauss map of X defined by embedded tangent spaces is separable, and moreover that the converse is not true in general. We prove that the converse holds under the assumption that X is of dimension two. Explaining the subtleness of the problem, we present an example of smooth projective surfaces in arbitrary positive characteristic, which gives a negative answer to a question raised by S. Kleiman and R. Piene on the inseparability of the Gauss map.

    Original languageEnglish
    Pages (from-to)699-703
    Number of pages5
    JournalMathematische Zeitschrift
    Volume256
    Issue number4
    DOIs
    Publication statusPublished - 2007 Aug

    Fingerprint

    Gauss Map
    Reflexivity
    Separability
    Converse
    Tangent Space
    Positive Characteristic
    Projective Variety
    Two Dimensions
    Arbitrary

    Keywords

    • Gauss map
    • Reflexive
    • Separable

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    The separability of the Gauss map and the reflexivity for a projective surface. / Fukasawa, Satoru; Kaji, Hajime.

    In: Mathematische Zeitschrift, Vol. 256, No. 4, 08.2007, p. 699-703.

    Research output: Contribution to journal › Article

    Fukasawa, S & Kaji, H 2007, 'The separability of the Gauss map and the reflexivity for a projective surface', Mathematische Zeitschrift, vol. 256, no. 4, pp. 699-703. https://doi.org/10.1007/s00209-006-0085-0
    Fukasawa S, Kaji H. The separability of the Gauss map and the reflexivity for a projective surface. Mathematische Zeitschrift. 2007 Aug;256(4):699-703. https://doi.org/10.1007/s00209-006-0085-0
    Fukasawa, Satoru ; Kaji, Hajime. / The separability of the Gauss map and the reflexivity for a projective surface. In: Mathematische Zeitschrift. 2007 ; Vol. 256, No. 4. pp. 699-703.
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