{"paper":{"title":"Dimension theory of the moduli space of twisted $k$-differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johannes Schmitt","submitted_at":"2016-07-28T12:43:39Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08429","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}