Related papers: On Kan fibrations for Maltsev algebras

We suggest a general framework for compactifing quasi-projective Lagrangian fibrations of geometric origin by holomorphic symplectic varieties. This framework includes a compactification criterion, which we then apply to various fibrations…

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

Let X be a normal connected complex algebraic variety equipped with a semisimple complex representation of its fundamental group. Then, under a maximality assumption, we prove that the covering space of X associated to the kernel of the…

This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-K\"ahler manifolds. We present four foundational results that extend well-known facts about isotrivial elliptic fibrations of K3 surfaces. First, we prove…

We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with…

Let $M$ be a holomorphic symplectic K\"ahler manifold equipped with a Lagrangian fibration $\pi$ with compact fibers. The base of this manifold is equipped with a special K\"ahler structure, that is, a K\"ahler structure $(I, g, \omega)$…

We prove that arbitrary simplicial manifolds satisfy Kan conditions in a suitable local sense. This allows us to expand a technique for differentiating higher Lie groupoids worked out in current research to the setting of general simplicial…

Classification questions are often about understanding components of a category. It is much more desirable however to be able to understand the entire homotopy type of this category and not just the set of its components. In this paper we…

We give a Hodge-theoretic proof of Hwang's theorem, which says that if the base of a Lagrangian fibration of an irreducible holomorphic symplectic manifold is smooth, it must be projective space.

In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the…

We prove that every non-degenerate toric variety, every homogeneous space of a connected linear algebraic group without non-constant invertible regular functions, and every variety covered by affine spaces admits a surjective morphism from…

We classify lagrangian fibrations on Nikulin orbifolds, a well studied class of singular irreducible holomorphic symplectic varieties, and prove they verify the SYZ conjecture.

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric…

The canonical map from the Kan subdivision of a product of finite simplicial sets to the product of the Kan subdivisions is a simple map, in the sense that its geometric realization has contractible point inverses.

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G/K\to G/L$ is a fibration. As an application of this, we obtain two…

We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie groupoids. Concretely, we set an equivalence between…

Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…

We prove that a Malcev algebra $\mathcal{M}$ containing the $7$-dimensional simple non-Lie Malcev algebra $\mathbb{M}$ such that $m\mathbb{M}\neq 0$ for any $m\neq 0$ from $\mathcal{M}$, is isomorphic to $\mathbb{M}\otimes_\textup{F}…

Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space is a compact ENR. The proof uses homotopy coherent…

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and in fact a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois…