Related papers: Noncommutative cyclic isolated singularities

We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$…

A set $M$ of nonzero integers is said to split a finite abelian group $G$ if there exists a subset $S\subseteq G$ such that $M\cdot S = G\setminus\{0\}$. Such a splitting is called purely singular if every prime divisor of $|G|$ divides…

We prove a general theorem showing that iterated skew polynomial extensions of the type which fit the conditions needed by Cauchon's deleting derivations theory and by the Goodearl-Letzter stratification theory are unique factorisation…

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for…

It is shown that for every splitting of a polynomial with noncommutative coefficients into linear factors $(X-a_{k})$ with $a_{k}$'s commuting with coefficients, any cyclic permutation of linear factors gives the same result and all $a_{k}$…

We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle.…

Let $(X,g)$ be a compact manifold with conic singularities. Taking $\Delta_g$ to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the singularities of the trace of the half-wave group $e^{- i t \sqrt{…

We consider the relationship between the relative stable category of Benson, Iyengar, and Krause and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is…

Let $d\geq3$ and $g\geq1$ be integers. Using a geometric construction involving the symmetric product of a projective curve, we exhibit a $d$-dimensional complete local normal domain over $\mathbb{C}$ with an isolated singularity such that…

We give a complete solution for the reduced Gromov-Witten theory of resolved surface singularities of type A_n, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the T-equivariant relative…

The class of nonlinear integral equations on the positive half-line with a monotone operator of Hammerstein type is studied. With various partial representations of the corresponding kernel and nonlinearity, this class of equations has…

We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalo (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and…

We consider a set $SPG(\mathcal{A})$ of pure split states on a quantum spin chain $\mathcal{A}$ which are invariant under the on-site action $\tau$ of a finite group $G$. For each element $\omega$ in $SPG(\mathcal{A})$ we can associate a…

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we extend a well-known result about the Picard group of a semisimple group to reductive…

We compare the so-called clock condition to the gradability of certain differential modules over quadratic monomial algebras. For a stably hereditary algebra or a gentle one-cycle algebra, these considerations show that the orbit category…

Given a principal fibre bundle with structure group $S$, and a fibre transitive Lie group $G$ of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps $\psi\colon \mathfrak{g}\rightarrow…

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing…

In [16] the fundamental relationship between stable quotient invariants and the B-model for local P2 in all genera was studied under some specialization of equivariant variables. We generalize the argument of [16] to full equivariant…

Algebraic $K$-theory is a homology theory that behaves very well on sufficiently nice objects such as stable $C^*$-algebras or smooth algebraic varieties, and very badly in singular situations. This survey explains how to exploit this to…

Let G/K be an irreducible Riemannian symmetric space of the non-compact type and denote by \Xi the associated crown domain. We show that for any proper action of a cyclic group \Gamma the quotient \Xi/\Gamma is Stein. An analogous statement…