Related papers: The (local) lifting problem for curves

The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…

This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

Criteria for a diffeomorphism of a smooth manifold $M$ to be lifted to a linear automorphism of a given real vector bundle $p\colon V\rightarrow M$, are stated. Examples are included and the metric and complex vector-bundle cases are also…

In this paper, we study locally analytic vectors in the "partially" completed cohomology of Shimura varieties associated with some rank $2$ unitary groups over a totally real field $F^+$ such that $F^+_v = \mathbb{Q}_{p^2}$ for some…

First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…

We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete…

Given a smooth hyperplane section $H$ of a rational homogeneous space $G/P$ with Picard number one, we address the question whether it is always possible to lift an automorphism of $H$ to the Lie group $G$, or more precisely to Aut$(G/P)$.…

We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an…

We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any…

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking…

In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main…

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…

We develop the theory of $L^2$-torsion of an automorphism of a group and compute it for every automorphism of a group which is hyperbolic and one-ended relative to a finite collection of virtually polycyclic groups. We also prove a…

For any real-analytic hypersurface M in complex euclidean space of dimension >= 2 which does not contain any complex-analytic subvariety of positive dimension, we show that for every point p in M the local real-analytic CR automorphisms of…

In this paper we prove several lifting theorems for morphisms of tropical curves. We interpret the obstruction to lifting a finite harmonic morphism of augmented metric graphs to a morphism of algebraic curves as the non-vanishing of…

We use height arguments to prove two results about the dynamical Mordell-Lang problem. (i) For an endomorphism of a projective variety, the return set of a dense orbit into a curve is finite if any cohomological Lyapunov multiplier of any…

The automorphism tower of a group is obtained by computing its automorphism group, the automorphism group of THAT group and so on, iterating transfinitely. Each group maps into the next using inner automorphisms and one takes a direct limit…