Related papers: On a toroidalization for klt singularities

We show that the quantum coordinate ring of a semisimple group is a unique factorisation domain in the sense of Chatters and Jordan in the case where the deformation parameter q is a transcendental element.

Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler…

We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…

An action of a group on a set is oligomorphic if it has finitely many orbits of $n$-element subsets for all $n$. We prove that for a large class of groups (including all groups of finite virtual cohomological dimension and all countable…

We present a simplicial model for gravity written in terms of a discretized Lorentz connection and a discretized tetrad field. The continuum limit of its action is Holst's action for general relativity. With the intention of using it to…

An \textit{algebraic} action of a discrete group $\Gamma $ is a homomorphism from $\Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $\Gamma $ is determined by a module…

We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the…

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with boundary) with nonzero Euler characteristic, integral homology…

We prove that a birational morphism of projective 3-folds, over a field of characteristic zero, can be made toroidal by performing a sequence of blow ups of points and nonsingular curves above the domain and target.

Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of…

We study simplicial action of groups on one vertex Kan complexes. We show that every semi-direct product of the fundamental group of an one vertex Kan complex with a finite group can be simplicially realized. We also calculate the…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

We establish birational superrigidity for a large class of singular projective Fano hypersurfaces of index one. In the special case of isolated singularities, our result applies for instance to: (1) hypersurfaces with semi-homogeneous…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this…

We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal $I$, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the…

For an algebraic torus $T$, the finite central extensions $G$ of $T$ are characterized in terms of ramification theory of regular actions of $G$ on Krull algebras over an algebraically closed base field $K$ of any characteristic.

We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…

We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the elliptic tangent bundle. Using this Lie algebroid, we…

An irreducible algebraic variety $X$ is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group $\text{Aut}(X)$ of a rigid affine variety contains a unique maximal torus…