Large characteristic subgroups of surface groups not containing any simple loops
We determine the largest (i.e. smallest index) characteristic subgroup of surface groups not containing any simple loops.
math.GT↗
arXiv subjects
Martin Pikaart
Publications and source records attributed to Martin Pikaart.
An orbifold partition of ${\overline{M}_g^n}$
We define a partition of ${\overline{M}_g^n}$ and show that the cohomology of ${\overline{M}_g^n}$ in a given degree admits a filtration whose respective quotients are isomorphic to the shifted cohomology groups of the parts if $g$ is sufficiently large. This implies that the map $H^k({\overline{M}_g^n}) \ra H^k(M_g^n)$ is onto and that the Hodge structure of $H^k(M_g^n)$ is pure of weight $k$ if $g \geq 2k+1$. Our main ingredient is the stability theorem of Harer and Ivanov.
alg-geom↗
Moduli of curves with non-abelian level structure
Following Deligne and Mumford we construct a coarse moduli space of smooth curves with non-abelian level structure, involving higher order commutators. We prove that its Deligne-Mumford compactification is smooth over an open part of Spec(${\msy Z}$).
alg-geom↗