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Turkish Journal of Mathematics

Authors

EDOARDO BALLICO

Abstract

A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of a connected stick figure (or any reduced and connected curve) $X\subset \mathbb{P}^r$ such that $\deg (X)=d$ and $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem of obtaining all arithmetic genera below the maximal one.

DOI

10.55730/1300-0098.3384

Keywords

Curves in projective spaces, stick figures, reducible curves, arithmetic genus

First Page

650

Last Page

663

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Mathematics Commons

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