Maximal gonality on strata of differentials and uniruledness of strata in low genus

We prove that for a generic element in nonhyperelliptic component of an abelian stratum $\mathcal{H}_g(\mu)$ genus $g$, the underlying curve has maximal gonality. extend this result to case quadratic strata when partition $\mu$ positive entries. As consequence we deduce all components $\mathcal{H}_9(\mu)$ are uniruled is 16 and $\mathcal{H}^2_g(\mu)$ $4g-4$ either $3\leq g\leq5$ or $g=6$ $l(\mu)\geq 4$.