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arXiv · 1908.01620

A note on $r$ hypersurfaces intersecting in $\mathbb{P}^r$

Dennis Tseng
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Abstract

We consider the locus of $r$-tuples of homogeneous forms of some fixed degree whose common vanishing locus in $\mathbb{P}^r$ is positive dimensional. We show that any component of maximal dimension of that locus either consists of homogeneous forms all vanishing on some line or homogeneous forms where a proper subset fail to intersect properly.

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Dennis Tseng. 2019-08-05. A note on $r$ hypersurfaces intersecting in $\mathbb{P}^r$. https://arxiv.org/abs/1908.01620

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