Curves and stick figures not contained in a hypersurface of a given degree. (English) Zbl 1509.14066
Summary: A stick figure \(X\subset\mathbb{P}^r\) is a nodal curve whose irreducible components are lines. For fixed integers \(r \geq 3\), \(s \geq 2\) 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.
MSC:
| 14H50 | Plane and space curves |
References:
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