Bounding Pinch Point Schemes of Projected Surfaces

Adam Cartisano; Anand Patel

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arXiv · 2207.07963

Bounding Pinch Point Schemes of Projected Surfaces

Adam Cartisano·Anand Patel

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Abstract

Let $X$ be a smooth surface and let $\varphi:X\to\mathbb{P}^N$, with $N\geq 4$, be a finitely ramified map which is birational onto its image $Y = \varphi(X)$, with $Y$ non-degenerate in $\mathbb{P}^N$. In this paper, we produce a lower bound for the length of the pinch scheme of a general linear projection of $Y$ to $\mathbb{P}^3.$ We then prove that the lower bound is realized if and only if $Y$ is a rational normal scroll.

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BibTeX RIS

Adam Cartisano, Anand Patel. 2022-07-16. Bounding Pinch Point Schemes of Projected Surfaces. https://arxiv.org/abs/2207.07963

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