Space curves not contained in low degree surfaces in positive characteristic


Let C \subset \mathbf{P}^3 be an integral projective curve not contained in a quadric surface. Set d:=deg(C),g:=p_a(C), 

\pi_1(d,3):= \left\{ d^2/6 - d/2 + 1 if d/3 \in \mathbf{Z} 
                              d^2/6 - d/2 + 1/3 if d/3 \notin \mathbf{Z} \right.

Here we prove in arbitrary characteristic that g \le \pi_1(d,3) if d \ge 25.

DOI Code: 10.1285/i15900932v20n2p27

Keywords: Integral projective curve; Singular space curve; Arithmetic genus; Quadric surface; Plane section; Hyperplane section; Hilbert function

Classification: 14H50

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