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Injective endomorphisms of algebraic and analytic sets

Sławomir Cynk, Kamil Rusek (1991)

Annales Polonici Mathematici

We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.

Multiple prime covers of the riemann sphere

Aaron Wootton (2005)

Open Mathematics

A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

On commutativity and ovals for a pair of symmetries of a Riemann surface

Ewa Kozłowska-Walania (2007)

Colloquium Mathematicae

We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry having g+1-q...

On reconstruction of polynomial automorphisms

Paweł Gniadek (1996)

Annales Polonici Mathematici

We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.

Problems from the workshop on Automorphisms of Curves (Leiden, August, 2004)

Gunther Cornelissen, Frans Oort (2005)

Rendiconti del Seminario Matematico della Università di Padova

In the week of August, 16th-20th of 2004, we organized a workshop about “Automorphisms of Curves” at the Lorentz Center in Leiden. The programme included two “problem sessions”. Some of the problems presented at the workshop were written down; this is our edition of these refereed and revised papers. Edited by Gunther Cornelissen and Frans Oort with contributions of I. Bouw; T. Chinburg; G. Cornelissen; C. Gasbarri; D. Glass; C. Lehr; M. Matignon; F. Oort; R. Pries; S. Wewers.

Riemann surfaces with a large abelian group of automorphisms.

Clelia Lomuto (2006)

Collectanea Mathematica

In this paper we classify all Riemann surfaces having a large abelian group of automorphisms, that is having an abelian group of automorphism of order strictly bigger then 4(g-1), where g denotes as usual the genus of the Riemann surface.

Structure du groupe de Grothendieck équivariant d’une courbe et modules galoisiens

Niels Borne (2002)

Bulletin de la Société Mathématique de France

Cet article est consacré à l’étude de la structure d’anneau du groupe de Grothendieck équivariant d’une courbe projective munie d’une action d’un groupe fini. On explicite cette structure en introduisant un groupe de classes de cycles à coefficients dans les caractères et une notion d’auto-intersection pour ces cycles. De ce résultat, on déduit une expression de la caractéristique d’Euler équivariante d’un G -faisceau.

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