Geodesic
Hyperelliptic classes are rigid and extremal in genus two
Épijournal de Géométrie Algébrique, Tome 4 (2020)

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We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell + m$) classes on $\overline{\mathcal{M}}_{2,\ell+2m+n}$. This generalizes work of Chen and Tarasca and establishes an infinite family of rigid and extremal classes in arbitrarily-high codimension. 
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     author = {Blankers, Vance},
     title = {Hyperelliptic classes are rigid and extremal in genus two},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     year = {2020},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2020.volume4.4902/}
}
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Blankers, Vance. Hyperelliptic classes are rigid and extremal in genus two. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2020.volume4.4902

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