Turkish Journal of Mathematics
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
Recommended Citation
BALLICO, E (2023). Curves and stick figures not contained in a hypersurface of a given degree. Turkish Journal of Mathematics 47 (2): 650-663. https://doi.org/10.55730/1300-0098.3384
