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We show that the strata $ \mathcal{M}_{11,6}(k) \subset \mathcal{M}_{11} $ of$ 6-$gonal curves of genus $ 11 $, equipped with $k$ mutually independent andtype I pencils of degree six, have a unirational irreducible component for$5\leq k\leq 9$. The unirational families arise from degree $ 9 $ plane curveswith $ 4 $ ordinary triple and $ 5 $ ordinary double points that dominate anirreducible component of expected dimension. We will further show that thefamily of degree $ 8 $ plane curves with $ 10 $ ordinary double points coversan irreducible component of excess dimension in $ \mathcal{M}_{11,6}(10) $.

The unirational components of the strata of genus $11$ curves with several pencils of degree $6$ in $\mathcal{M}_{11}$