Finite sets of points in ${\mathbb {P}}^4$ with special projection properties

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发表日期：

2025年2月25日

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Luca Chiantini,
Łucja Farnik,
Giuseppe Favacchio,
Brian Harbourne,
Juan Migliore,
Tomasz Szemberg,
Justyna Szpond

摘要

In this note we introduce the notion of (b, d)-geprofi sets and study their basic properties. These are sets of bd points in $ {\mathbb {P}}^4$ $P^{4}$ whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree b and a surface of degree d. We show that such nontrivial sets exist if and only if $b\ge 4$ $b \geq 4$ and $d\ge 2$ $d \geq 2$ . Somewhat surprisingly, for infinitely many values of b and d there exist such sets in linear general position. The note contains open questions and problems.

Finite sets of points in \({\mathbb {P}}^4\) with special projection properties

摘要