Related papers: Quasihomogeneous analytic affine connections on su…

Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f:Y -> X be a map of K-affinoid varieties. We prove that for each point x in X, either f is flat at x, or there exists, at least locally around x, a…

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

The classification, up to a center-affinity, of the homogeneous quadratic differential systems defined on $\mathbb{R}^{3}$ that have at least a semisimple derivation with one-dimensional kernel, is achieved. It is proved that there exist 35…

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable…

We show that any two homogeneous affine semigroups can be glued by embedding them suitably in a higher dimensional space. As a consequence, we show that the sum of their homogeneous toric ideals is again a homogeneous toric ideal, and that…

This paper applies the recently developed framework of cohomologically calibrated affine connections to the fundamental problem of constructing non-Riemannian Einstein manifolds. In this framework, the torsion of a connection is…

We prove that a meromorphic mapping, which sends a peace of a real analytic strictly pseudoconvex hypersurface in $\cc^2$ to a compact subset of $\cc^N$ which doesn't contain germs of non-constant complex curves is continuous from the…

We study open analytic curves over non-archimedian fields and their formal models. In particular, we give a criterion, in terms of etale cohomology, when such a formal model is (almost) semistable.

Let $(G,H,\sigma)$ be a symmetric pair and $\mathfrak{g}=\mathfrak{m}\oplus\mathfrak{h}$ the canonical decomposition of the Lie algebra $\mathfrak{g}$ of $G$. We denote by ${\nabla}^0$ the canonical affine connection on the symmetric space…

We show that through a point of an affine variety there always exists a smooth plane curve inside the ambient affine space, which has the multiplicity of intersection with the variety at least 3. This result has an application to the study…

We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…

The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$.…

Let $V$ be a complete discrete valuation ring with fraction field $F$ of characteristic zero and with residue field $\mathbb{F}$. We introduce analytic cyclic homology of complete torsion-free bornological algebras over $V$. We prove that…

We prove that every local complete intersection curve in $Spec(A)$, where $A$ is a commutative Noetherian ring of dimension three, is a set-theoretic complete intersection. An analogous result is established for local complete intersection…

A branched affine structure on a compact topological surface with marked points is a complex affine structure outside the marked points. We give a proof of an unpublished foundational theorem of Veech, stating that any branched affine…

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…

We examine complements (inside products of a smooth projective complex curve of arbitrary genus) of unions of diagonals indexed by the edges of an arbitrary simple graph. We use Gysin models associated to these quasi-projective manifolds to…

We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no…

An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution…