Related papers: Desingularization of binomial varieties using tori…
We study Hom 2-functors parameterizing 1-morphisms of algebraic stacks, and prove that it is representable by an algebraic stack under certain conditions, using Artin's criterion. As an application we study Picard 2-functors which…
In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation…
We show that a toroidal morphism can be reduced to a weakly semistable one in a universal way if we allow families to be modified to Deligne-Mumford stacks instead of schemes.
We review different scenarios for the motion and merging of Dirac points in two dimensional crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point.…
Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for…
We extend the Cox-Hu-Keel construction of the Cox rings to any proper birational morphisms of normal noetherian schemes. It allows the representation of any proper birational morphism by a map of schemes with mild singularities with torus…
We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of "atypical points" at infinity. We construct an effective algorithm with low complexity in order to detect…
We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
We give a new description of the data needed to specify a morphism from a scheme to a toric Deligne-Mumford stack. The description is given in terms of a collection of line bundles and sections which satisfy certain conditions. As…
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…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the…
In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on…
This paper is devoted to the factorization of multivariate polynomials into products of linear forms, a problem which has applications to differential algebra, to the resolution of systems of polynomial equations and to Waring decomposition…
By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent…
We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is…
A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite…