Positivity of line bundles on general blow ups of Hirzebruch surfaces

Abstract

We investigate various positivity properties of line bundles on general blow ups of Hirzebruch surfaces motivated by \cite{Han}, where the author has studied general blow ups of ${\mathbb{P}}^2$. For each of the properties: ampleness, global generation, very ampleness, and $k$-very ampleness, we provide several sufficient numerical conditions.

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