Curves contracted by the Gauss map

Lei Song

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arXiv · 2103.11159

Curves contracted by the Gauss map

Lei Song

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Abstract

Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show that if the variety is normal, then a contracted line always has local obstruction for the embedded deformation and each component of the Hilbert scheme where the line lies is non-reduced everywhere.

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Lei Song. 2021-03-20. Curves contracted by the Gauss map. https://arxiv.org/abs/2103.11159

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