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arXiv · 2603.21518

On the discriminant locus of a generic projection

Si-Yang Liu·Yilong Zhang
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Abstract

For a smooth projective variety $X\subseteq \mathbb P^N$ over an algebraically closed field of char $0$, we show that the discriminant locus of a generic projection of $X$ is projectively dual to a general linear section of the dual variety, and deduce a purity statement for the discriminant. Over $\mathbb C$, we also show that the fundamental group of the complement of the branch divisor arising from generic projection of a normal hypersurface surjects onto a braid group via braid monodromy.

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Si-Yang Liu, Yilong Zhang. 2026-03-23. On the discriminant locus of a generic projection. https://arxiv.org/abs/2603.21518

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