Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3384
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.
Keywords
Curves in projective spaces, stick figures, reducible curves, arithmetic genus
First Page
650
Last Page
663
Recommended Citation
BALLICO, EDOARDO
(2023)
"Curves and stick figures not contained in a hypersurface of a given degree,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 16.
https://doi.org/10.55730/1300-0098.3384
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/16
