Jorgensen's inequality for non-Archimedean metric spaces.

Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an application, we give a version of Jørgensen’s inequality for SL(2, ℚ p )

Del Pezzo surfaces of degree 1 and jacobians

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.Comment: 24 page

Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

q-Deformed Conformal Quantum Mechanics

We construct a q-deformed version of the conformal quantum mechanics model of de Alfaro, Fubini and Furlan for which the deformation parameter is complex and the unitary time evolution of the system is preserved. We also study differential calculus on the q-deformed quantum phase space associated with such system.Comment: 10 pages, LaTeX, revised version with minor corrections to appear in Phys. Rev.

The Abelian/Nonabelian Correspondence and Frobenius Manifolds

We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ``abelianized'' quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.Comment: 35 pages, no figure

Differential calculus and gauge transformations on a deformed space

Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf algebra, thus we can represent a twisted Hopf algebra on deformed spaces. That leads to the construction of Lagrangian invariant under a twisted Lie algebra.Comment: 14 pages, to appear in General Relativity and Gravitation Journal, Obregon's Festschrift 2006, V2: misprints correcte

q-Deformed Superalgebras

The article deals with q-analogs of the three- and four-dimensional Euclidean superalgebra and the Poincare superalgebra.Comment: 38 pages, LateX, no figures, corrected typo

Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.Comment: 35 pages, references added, slightly revised introductio

On A Superfield Extension of The ADHM Construction and N=1 Super Instantons

We give a superfield extension of the ADHM construction for the Euclidean theory obtained by Wick rotation from the Lorentzian four dimensional N=1 super Yang-Mills theory. In particular, we investigate the procedure to guarantee the Wess-Zumino gauge for the superfields obtained by the extended ADHM construction, and show that the known super instanton configurations are correctly obtained.Comment: 22 pages, LaTeX, v2: typos corrected, references adde

The Ricci flow on noncommutative two-tori

In this paper we construct a version of Ricci flow for noncommutative 2-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss-Bonnet theorem for noncommutative tori.Comment: 18 pages, LaTe