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.

Curves and stick figures not contained in a hypersurface of a given degree / Ballico, Edoardo. - In: TURKISH JOURNAL OF MATHEMATICS. - ISSN 1300-0098. - ELETTRONICO. - 47:2(2023), pp. 650-663. [10.55730/1300-0098.3384]

Curves and stick figures not contained in a hypersurface of a given degree

Ballico, Edoardo
Primo
2023-01-01

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.
2023
2
Ballico, Edoardo
Curves and stick figures not contained in a hypersurface of a given degree / Ballico, Edoardo. - In: TURKISH JOURNAL OF MATHEMATICS. - ISSN 1300-0098. - ELETTRONICO. - 47:2(2023), pp. 650-663. [10.55730/1300-0098.3384]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/400095
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