Abelian differentials with prescribed singularities

no code implementations • 4 Mar 2021 • Quentin Gendron, Guillaume Tahar

The main result of this paper is that with few exceptions, every pattern of orders and residues can be obtain by an Abelian differential.

Geometric Topology Algebraic Geometry

Towards a classification of connected components of the strata of $k$-differentials

no code implementations • 5 Jan 2021 • Dawei Chen, Quentin Gendron

A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical bundle.

Geometric Topology Algebraic Geometry Number Theory

The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of $Ω\mathcal{M}_{g}$

no code implementations • 11 Mar 2015 • Quentin Gendron

The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials.

Algebraic Geometry Geometric Topology 14H10 (Primary) 14H45, 32J25 (Secondary)