Abstract
A projective variety whose Gauss map has positive dimensional fibres corresponds to a special kind of scroll called Gaussian. A Gaussian scroll is a member of a canonical derived Gaussian flag. We introduce a duality in the class of Gaussian scrolls and flags and study its consequences. In particular, a Gaussian scroll is dual to the derived or tangent developable scroll of a Gaussian scroll in the dual projective space, and is the ’leading edge’ or antiderived scroll of its derived stationary scroll.
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Notes
We thank Dr. L. Song for bringing the paper [2] to our attention.
The terminology is chosen to avoid confusion with dual variety.
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Acknowledgements
We thank Professor E. Mezzetti and Professor O. Tommasi for helpful comments and references.
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Ziv Ran is the sole author of this work and is solely responsible for its content.
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Ran, Z. Gaussian scrolls, Gaussian flags and duality. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01023-5
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DOI: https://doi.org/10.1007/s12215-024-01023-5