Related papers: Logarithmic Cartan geometry on complex manifolds
Given a coherent sheaf E on a scheme of finite type X over a perfect field, we introduce a category of complexes of \'etale sheaves on X with logarithmic conductors bounded by E and study its compatibilities with finite push-forward.
The aim of this paper is to study the structure of the higher-dimensional Teichm\"uller and Riemann moduli spaces, viewed as stacks over the category of complex manifolds. We first show that the space of complex operators on a smooth…
In this paper, we present foundational material towards the development of a rigorous enumerative theory of stable maps with Lagrangian boundary conditions, ie stable maps from bordered Riemann surfaces to a symplectic manifold, such that…
Using factorizable Hopf algebras, we construct modular invariant partition functions of charge conjugation, or Cardy, type as characters of coends in categories that share essential features with the ones appearing in logarithmic CFT. The…
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…
We introduce a systematic method to solve a type of Cartan's realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as…
We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics transverse to the foliation. In order to develop the necessary…
We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real…
Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as…
We construct Lie algebras of derivations (and identify their geometrical realization) whose Maurer-Cartan sets provide moduli spaces describing the classes of homotopy types of rational spaces sharing either the same homotopy Lie algebra,…
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…
We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…
We introduce and investigate multicomplex configurations, a class of projective varieties constructed via specialization of the polarizations of Artinian monomial ideals. Building upon geometric polarization and geometric vertex…
Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry,…
We present the topological foundations for the solvability of Multiplicative Cousin problems formulated on an axially symmetric domain $\Omega \subset \mathbb H.$ In particular, we provide a geometric construction of quaternionic Cartan…
The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of…
By a recent result of Viehweg, projective manifolds with ample canonical class have a coarse moduli space, which is a union of quasiprojective varieties. In this paper, we prove that there are manifolds with ample canonical class that lie…
The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and…
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space…
We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other…