The strata of abelian differentials with prescribed zeros are interesting objects of study from Teichmuller dynamics point of view. Their connected components have been classified by Kontsevich-Zorich using spin and hyperelliptic structures. In this talk, I will introduce a compactification of these strata using logarithmic geometry. We show that such compactification distinguishes spin parities over the boundary. Furthermore, we show that our construction Combined with admissible covers provides a toroidal compactification of the hyperelliptic component and the hyperelliptic loci of the strata.
Speaker(s): Qile Chen (Boston College)