Geodesic
The unirational components of the strata of genus $11$ curves with several pencils of degree $6$ in $\mathcal{M}_{11}$
Documenta mathematica, Tome 26 (2021), pp. 415-438.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We show that the strata $\mathcal{M}_{11,6}(k)\subset \mathcal{M}_{11,6}$ of $6$-gonal curves of genus $11$, equipped with $k$ mutually independent and type I pencils of degree six, have a unirational irreducible component for $5\leq k\leq 9$. The unirational families arise from degree $9$ plane curves with $4$ ordinary triple and $5$ ordinary double points that dominate an irreducible component of expected dimension. We will further show that the family of degree $8$ plane curves with $10$ ordinary double points covers an irreducible component of excess dimension in $\mathcal{M}_{11,6}(10)$.
Classification : 14H10, 14H51, 14Q05, 14M20, 32G05
Keywords: unirationality, deformation, Koszul divisor, Brill-Noether 
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     title = {The unirational components of the strata of genus \(11\) curves with several pencils of degree \(6\) in {\(\mathcal{M}_{11}\)}},
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Keneshlou, Hanieh; Schreyer, Frank-Olaf. The unirational components of the strata of genus \(11\) curves with several pencils of degree \(6\) in \(\mathcal{M}_{11}\). Documenta mathematica, Tome 26 (2021), pp. 415-438. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a47/