On the effective cone of higher codimension cycles in $\overline{\mathcal{M}}_{g,n}$

Scott Mullane

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arXiv · 1710.09044

On the effective cone of higher codimension cycles in $\overline{\mathcal{M}}_{g,n}$

Scott Mullane

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Abstract

We exhibit infinitely many extremal effective codimension-$k$ cycles in $\overline{\mathcal{M}}_{g,n}$ in the cases $g\geq 3, n\geq g-1$ and $k=2$, $g\geq 2$, $k\leq n-g,g,$ and $g=1$, $k\leq n-2$. Hence in these cases the effective cone is not rational polyhedral.

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Scott Mullane. 2017-10-25. On the effective cone of higher codimension cycles in $\overline{\mathcal{M}}_{g,n}$. https://arxiv.org/abs/1710.09044

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