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Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smoothcurve and let $E_1$, $E_2$ be vector bundles over $C$. In this paper, we extendthe results in \cite{K-M-R} by computing the nef cone of $X$ withoutrestriction on the rank or semistability of $E_1$ and $E_2$. We also study theSeshadri constants of ample line bundles on $X$. We calculate the Seshadriconstants in some cases and give bounds in some of the remaining cases.

Nef cone and Seshadri constants on products of projective bundles over curves