Dimension Theory of the Moduli Space of Twisted $K$-Differentials
Documenta mathematica, Tome 23 (2018), pp. 871-894
In this note we extend the dimension theory for the spaces Hgk(μ) of twisted k-differentials defined by Farkas and Pandharipande in [G. Farkas and R. Pandharipande, J. Inst. Math. Jussieu 17, No. 3, 615–672 (2018; Zbl 06868654)] to the case k>1. In particular, we show that the intersection Hgk(μ)=Hgk(μ)∩Mg,n is a union of smooth components of the expected dimensions for all k≥0. We also extend a conjectural formula from [Zbl 06868654] for a weighted fundamental class of Hgk(μ) and provide evidence in low genus. If true, this conjecture gives a recursive way to compute the cycle class [Hgk(μ)] of the closure of Hgk(μ) for k≥1,μ arbitrary.
Classification :
14H10, 30F30
Mots-clés : deformation theory, strata of k-differentials, tautological classes, double ramification cycles
Mots-clés : deformation theory, strata of k-differentials, tautological classes, double ramification cycles
@article{10_4171_dm_637,
author = {Johannes Schmitt},
title = {Dimension {Theory} of the {Moduli} {Space} of {Twisted} $K${-Differentials}},
journal = {Documenta mathematica},
pages = {871--894},
year = {2018},
volume = {23},
doi = {10.4171/dm/637},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/637/}
}
Johannes Schmitt. Dimension Theory of the Moduli Space of Twisted $K$-Differentials. Documenta mathematica, Tome 23 (2018), pp. 871-894. doi: 10.4171/dm/637
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