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arXiv · 1607.08429

Dimension theory of the moduli space of twisted $k$-differentials

Johannes Schmitt
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Abstract

In this note we extend the dimension theory for the spaces $\widetilde{\mathcal H}_g^k(\mu)$ of twisted $k$-differentials defined by Farkas and Pandharipande in [FP15] to the case $k>1$. In particular, we show that the intersection $\widetilde{\mathcal H}_g^k(\mu) \cap \mathcal{M}_{g,n}$ is a union of smooth components of the expected dimensions for all $k\geq 0$. We also extend a conjectural formula from [FP15] for a weighted fundamental class of $\widetilde{\mathcal H}_g^k(\mu)$ and provide evidence in low genus.

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Johannes Schmitt. 2016-07-28. Dimension theory of the moduli space of twisted $k$-differentials. https://arxiv.org/abs/1607.08429

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