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- Title
On the space curves with the same image under the gauss maps.
- Authors
Kaji, Hajime
- Abstract
From an irreducible complete immersed curve X in a projective space ℙ other than a line, one obtains a curve X in a Graasmann manifold G of lines in ℙ that is the image of X under the Gauss map, which is defined by the embedded tangents of X. The main result of this article clarifies in case of positive characteristic what curves X have the same X′: It is shown that X is uniquely determined by X′ if X, or equivalently X′, has geometric genus at least two, and that for curves X and X with X ≠ X in ℙ, if X′ = X′ in G and either X or X is reflexive, then both X and X are rational or supersingular elliptic; moreover, examples of smooth X and X in that case are given.
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p249
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026550