98 citations · 153 across the 13 of their papers we have counts for
15 papers
Finite isoresidual covers in strata of -differentials
Dawei Chen, Quentin Gendron, Miguel Prado +1
Consider the strata of primitive -differentials on the Riemann sphere whose singularities, except for two, are poles of order divisible by . The map that assigns to each -…
Isoresidual curves
Dawei Chen, Quentin Gendron, Miguel Prado +1
Given a partition of , the stratum parametrizes meromorphic differential one-forms on the Riemann sphere with~ zeros and poles of…
The space of solvable Pell-Abel equations
Andrei Bogatyrev, Quentin Gendron
Pell-Abel equation is a functional equation of the form P^{2}-DQ^{2} = 1, with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell-…
K-differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
We study the local invariants that a meromorphic -differential on a Riemann surface of genus can have for . These local invariants include the orders of zer…
Dihedral monodromy of cone spherical metrics
Quentin Gendron, Guillaume Tahar
Among metrics of constant positive curvature on a punctured compact Riemann surface with conical singularities at the punctures, dihedral monodromy means that the action of the mon…
Quadratic differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
The local invariants of a meromorphic quadratic differential on a compact Riemann surface are the orders of zeros and poles, and the residues at the poles of even orders. The main…
Abelian differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
The local invariants of a meromorphic Abelian differential on a Riemann surface of genus are the orders of zeros and poles, and the residues at the poles. The main result of th…
Towards a classification of connected components of the strata of -differentials
Dawei Chen, Quentin Gendron
A -differential on a Riemann surface is a section of the -th power of the canonical bundle. Loci of -differentials with prescribed number and multiplicities of zeros and p…
Équation de Pell-Abel et applications
Quentin Gendron
In this paper, we show that there are solutions of every degree of the equation of Pell-Abel on some real hyperelliptic curve of genus if and only if . This result,…
Isoresidual fibration and resonance arrangements
Quentin Gendron, Guillaume Tahar
The stratum of meromorphic -forms with a zero of order and poles of orders on the Riemann sphere has a map, the isor…
On the locus of genus curves that admit meromorphic differentials with a zero of order and a pole of order
Abel Castorena, Quentin Gendron
The main goal of this article is to compute the class of the divisor of obtained by taking the closure of the image of by the forg…
The moduli space of multi-scale differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space o…
Strata of -differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
A -differential on a Riemann surface is a section of the -th power of the canonical line bundle. Loci of -differentials with prescribed number and multiplicities of zeros…
Compactification of strata of abelian differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of s…
The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of
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. This allows us to compute the Kodaira…