Related papers: Noncommutative cyclic isolated singularities

Let A be a dg category, F:A->A a dg functor inducing an equivalence of categories in degree-zero cohomology, and A/F the associated dg orbit category. For every A1-homotopy invariant (e.g. homotopy K-theory, K-theory with coefficients,…

This paper applies the decomposition theorem in intersection cohomology to geometric invariant theory quotients, relating the intersection cohomology of the quotient to that of the semistable points for the action. Suppose a connected…

Let ${\cal K}_1(G)$ denote the inverse subsemigroup of ${\cal K}(G)$ consisting of all right cosets of all non-trivial subgroups of $G$. This paper concentrates on the study of the group $\Sigma({\cal K}_1(G))$ of all units of the…

We study two-dimensional cyclic quotient singularities defined by $k$-Wahl chains, a class of Hirzebruch--Jung continued fractions obtained inductively starting from $[k+2]$. This class includes the classical Wahl singularities in the case…

The article investigates the following question: given a projective variety X acted on by a connected and reductive group G, which is the relationship between the Gromov-Witten invariants of X and those of X//G? In this study we shall also…

This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree $2$. % Let $\mathsf{G}$ be a finite abelian group, $\mathbb{F}$ a field of characteristic zero and $\mathfrak{A}$ a…

We establish a version of Kn\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and…

This is an expository article on the noncommutative singularity theory of power series in noncommuting variables, its motivation from deformation theory, and its applications to contractibility of curves and the classification of smooth…

For an associative ring $R$ with identity, we study the absence of $k$-torsion in NK_1GQ(R); Bass nil-groups for the general quadratic or Bak's unitary groups. By using a graded version of Quillen--Suslin theory we deduce an analog for the…

We prove congruence relations modulo cyclotomic polynomials for multisums of $q$-factorial ratios, therefore generalizing many well-known $p$-Lucas congruences. Such congruences connect various classical generating series to their…

In an unpublished lecture note, J. Brian\c{c}on observed that if $\{f_t\}$ is a family of isolated complex hypersurface singularities such that the Newton boundary of $f_t$ is independent of $t$ and $f_t$ is non-degenerate, then the…

We develop an algorithm to test whether a non-CM elliptic curve $E/\mathbb{Q}$ gives rise to an isolated point of any degree on any modular curve of the form $X_1(N)$. This builds on prior work of Zywina which gives a method for computing…

We present a method for computing $\mathbb{A}^1$-homotopy invariants of singularity categories of rings admitting suitable gradings. Using this we describe any such invariant, e.g. homotopy K-theory, for the stable categories of…

Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A\star_{\alpha}\mathcal{G}$ can be realized as a partial skew group ring.…

Using Newton polyhedra and non-degeneracy of matrices we present conditions which guarantee the Whitney equisingularity of families of isolated determinantal singularities.

We say a closed point $x$ on a curve $C$ is sporadic if $C$ has only finitely many closed points of degree at most $\operatorname{deg}(x)$ and that $x$ is isolated if it is not in a family of effective degree $d$ divisors parametrized by…

A cone singularity is a normal affine variety $X$ with an effective one-dimensional torus action with a unique fixed point $x\in X$ which lies in the closure of any orbit of the $k^*$-action. In this article, we prove a boundedness theorem…

We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular…

For a cyclic group $G$ acting on a smooth variety $X$ with only one character occurring in the $G$-equivariant decomposition of the normal bundle of the fixed point locus, we study the derived categories of the orbifold $[X/G]$ and the…

Based on the Decay and Fission Conjecture, we provide a classification of unitary quivers whose 3d $\mathcal{N}=4$ Coulomb branches exhibit isolated singularities. This yields the complete list of isolated conical symplectic singularities…