Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Gendron, Quentin"'
Autor:
Gendron, Quentin
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G9, Pp 975-992 (2022)
In this paper, we show that there are solutions of degree $r$ of the equation of Pell–Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$. This result, which is known to the experts, has consequences, which seem to be unknown
Externí odkaz:
https://doaj.org/article/57d13653937c4008b1bc455d82b90bcd
Autor:
Gendron, Quentin
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 2, Pp 197-200 (2020)
This note gives an elementary proof that the strata of abelian differentials do not contain complete algebraic varieties.
Externí odkaz:
https://doaj.org/article/25ff8965908f4c0bb859851eb3113917
Autor:
Bogatyrev, Andrei, Gendron, Quentin
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-Abel equations with the fixed degrees of D and of a primitive solution
Externí odkaz:
http://arxiv.org/abs/2306.00884
Autor:
Gendron, Quentin, Tahar, Guillaume
We study the local invariants that a meromorphic $k$-differential on a Riemann surface of genus $g \geq 0$ can have for $k \geq 3$. These local invariants include the orders of zeros and poles, as well as the $k$-residues at the poles. We show that f
Externí odkaz:
http://arxiv.org/abs/2208.11654
Autor:
Gendron, Quentin, Tahar, Guillaume
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 monodromy group globally preserves a pair of antipodal points. Using rece
Externí odkaz:
http://arxiv.org/abs/2112.00594
Autor:
Gendron, Quentin, Tahar, Guillaume
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 result of this paper is that with few exceptions, every pattern of loc
Externí odkaz:
http://arxiv.org/abs/2111.12653
Autor:
Gendron, Quentin, Tahar, Guillaume
The local invariants of a meromorphic Abelian differential on a Riemann surface of genus $g$ are the orders of zeros and poles, and the residues at the poles. The main result of this paper is that with few exceptions, every pattern of orders and resi
Externí odkaz:
http://arxiv.org/abs/2103.03165
Autor:
Chen, Dawei, Gendron, Quentin
A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification for the moduli space of $k$-differe
Externí odkaz:
http://arxiv.org/abs/2101.01650
Autor:
Gendron, Quentin
In this paper, we show that there are solutions of every degree $r$ of the equation of Pell-Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$. This result, which is known to the experts, has consequences, which seem to be unk
Externí odkaz:
http://arxiv.org/abs/2010.09915
Autor:
Gendron, Quentin, Tahar, Guillaume
The stratum $\mathcal{H}(a,-b_{1},\dots,-b_{p})$ of meromorphic $1$-forms with a zero of order $a$ and poles of orders $b_{1},\dots,b_{p}$ on the Riemann sphere has a map, the isoresidual fibration, defined by assigning to any differential its residu
Externí odkaz:
http://arxiv.org/abs/2007.14872