Curves on a quadric surface over $\overline{\mathbb {F}}_p$
Keywords:
quadric surface, bihomogeneous polynomial, curve in a quadric surfaceAbstract
Here (following a paper by Giuffida, Maggioni and Re) we study the existence of curve $C\in \vert \mathcal {O}_{\mathbb {P}^1\times \mathbb {P}^1}(a,b)\vert$defined over small fields and with $h^0(C,\mathcal {O}_C(x,y))\cdot h^1(C, \mathcal {O}_C(x,y))=0$ for all integers $x, y$ such that $x\ge a$ and $y\le -2$.
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