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## On monodromy groups of del Pezzo surfaces

We show that the monodromy group acting on $H^1(\cdot,\mathbb Z)$ of a smooth   hyperplane section of a del Pezzo surface over $\mathbb C$ is the entire   group $\mathrm{SL}_2(\mathbb Z)$. For smooth surfaces with $b_1=0$ and hyperplane section   of genus $g>2$, there exist examples in which a similar assertion is   false. Actually, if hyperplane sections of a smooth surface are   hyperelliptic curves of genus $g\ge3$, then the monodromy group   acting on the integer $H^1$ on hyperplane sections is a proper   subgroup of $\mathrm{Sp}_{2g}(\mathbb Z)$.