The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of $\Omega {\mathcal{M}}_g$

Abstract

The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian differentials. The main ingredients to study the compactifications of the strata are a version of the plumbing cylinder construction for differential forms and an extension of the parity of the connected components of the strata to the differentials on curves of compact type. We study in detail the compactifications of the hyperelliptic minimal strata and of the odd minimal stratum in genus three.

58 pages, 5 figures

References in corpus (3)

• Compactification of strata of abelian differentials
• The moduli space of twisted canonical divisors
• Degenerations of Abelian Differentials

Cited by in corpus (8)

• Compactification of strata of abelian differentials
• Cohomology classes of strata of differentials
• GL(2,R)-Invariant Measures in Marked Strata: Generic Marked Points, Earle-Kra for Strata, and Illumination
• General Variational Formulas for Abelian Differentials
• The WYSIWYG compactification
• Hyperelliptic Gorenstein curves and logarithmic differentials
• Coarse density of subsets of $M_g$
• Maximal gonality on strata of differentials and uniruledness of strata in low genus