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arXiv · 2010.10807

Birational geometry of defective varieties, II

Edoardo Ballico·Claudio Fontanari
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Abstract

Let $X \subset \mathbb{P}^r$ be smooth and irreducible and for $k \ge 0$ let $\nu_k(X)$ (resp., $\delta_k(X)$) be the $k$-th contact (resp., the $k$-th secant) defect of $X$. For all $k \ge 0$ we have the inequality $\nu_k(X) \ge \delta_k(X)$ and in the case $k=1$ we characterize projective varieties $X$ for which equality holds, $\dim \mathrm{Sing}(X) \le \delta _1(X) -1$ and the generic tangential contact locus is reducible.

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Edoardo Ballico, Claudio Fontanari. 2020-10-21. Birational geometry of defective varieties, II. https://arxiv.org/abs/2010.10807

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