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arxiv: 2301.09215 · v2 · pith:JRXMCHVV · submitted 2023-01-22 · math.AG · math.CO

Existence of pencils with nonblocking hypersurfaces

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keywords mathbbhypersurfacespencilblockingdegreeeveryexistencefield
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We prove that there is a pencil of hypersurfaces in $\mathbb{P}^n$ of any given degree over a finite field $\mathbb{F}_q$ such that every $\mathbb{F}_q$-member of the pencil is not blocking with respect to $\mathbb{F}_q$-lines.

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