Abstract
We exhibit infinitely many extremal effective codimension-k cycles in \(\overline{\mathcal {M}}_{g,n}\) in the cases
\(g\ge 3, n\ge g-1\) and \(k=2\),
\(g\ge 2\), \(k\le \min (n-g,g),\) and
\(g=1\), \(k\le n-2\).
Hence in these cases the effective cone is not rational polyhedral.
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Mullane, S. On the effective cone of higher codimension cycles in \(\overline{\mathcal {M}}_{g,n}\). Math. Z. 295, 265–288 (2020). https://doi.org/10.1007/s00209-019-02344-3
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DOI: https://doi.org/10.1007/s00209-019-02344-3