相关论文: A cusp singularity with no Galois cover by a compl…

Every normal complex surface singularity with $\mathbb Q$-homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian cover of a rational or minimally elliptic singularity is a…

For each nonsingular hyperelliptic curve of arbitrary genus, we construct a natural injection from the Galois cohomology of 2-torsion subgroups of Jacobian varieties of the curve to the set of isomorphism classes of nonsingular complete…

It is shown that any finite complete covering of a non-commutative algebra in the sense of Calow and Matthes (J. Geom. Phys. 32 (2000), 114--165) gives rise to a Galois coring.

The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singularity, branched only at the singular point, is a complete…

Let A be a basic finite dimensional and connected algebra over an algebraically closed field k with zero characteristic. If the ordinary quiver of A has no double bypasses, we show that A admits a Galois covering which satisfies a universal…

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo-Velasco, Melle-Hernandez and Nemethi, thereby providing…

We introduce a notion of strict complete intersections with respect to Cox rings and we prove Galois descent for this new notion.

Applying geometric methods of $2$-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite…

A wide range of equations related to free surface motion in two dimensions exhibit the formation of cusp singularities either in time, or as function of a parameter. We review a number of specific examples, relating in particular to fluid…

In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…

A cusp singularity is an elliptic surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. In 1981, Looijenga proved that whenever a cusp…

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a…

We generalize Looijenga's conjecture for smoothing surface cusp singularities to the equivariant setting. Moreover, we prove that for any cusp singularity which admits a one-parameter smoothing, the smoothing can always be induced by…

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we…

The Zilber-Pink conjecture predicts that an algebraic curve in $\mathcal{A}_2$ has only finitely many intersections with the special curves, unless it is contained in a proper special subvariety. Under a large Galois orbits hypothesis, we…

In this note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $p>0$ in the case of abelian Galois groups of type…

This article computes the Galois groups of congruence covers arising in the context of certain hyperbolic triangle groups. As a consequence of this computation, the genera of the respective curves are deduced.

We introduce the concept of a Galois covering of a pointed coalgebra. The theory developed shows that Galois coverings of pointed coalgebras can be concretely expressed by smash coproducts using the coaction of the automorphism group of the…

We study the algebraic monodromy of families of cyclic Galois coverings of curves. Under a condition on the $G$-decomposition of the associated variation of Hodge structures, we prove a criterion for the maximality of the monodromy. The…

The main result of this article proves the nonvanishing of cuspidal cohomology for $GL(n)$ over a number field which is Galois over its maximal totally real subfield. The proof uses the internal structure of a strongly-pure weight that can…