Boris Tsvelikhovskiy

activity

20182025

collaborators

5 papers

math.AG2025

Notes from a family of smooth $G$ -Hilbert schemes

Boris Tsvelikhovskiy

Let $G = Z / r Z$ be the cyclic group of order $r$ , and let $ϖ = e^{2 π i / r}$ denote a primitive $r$ th root of unity. Consider the action of $G$ on $\mathbb{C…

math.AG2025

On a Dichotomy for Skyscraper Sheaves under the Bridgeland-King-Reid Equivalence

Boris Tsvelikhovskiy

Let $G \subset S L_{3} (C)$ be a finite abelian subgroup, and let $Y = G - Hilb (C^{3})$ be the corresponding $G$ -Hilbert scheme. Denote by $Ψ: D^b…

math.RT2019

On Poincare polynomials of shuffle algebra representations

Boris Tsvelikhovskiy

In this paper we study some combinatorial properties of the shuffle algebra $S_{q_{1}, q_{2}}$ with two complex parameters and, in particular, obtain the Hilbert series for $S_{q_{1…

math.RT2019

On categories $O$ of quiver varieties overlying the bouquet graphs

Boris Tsvelikhovskiy

We study representation theory of quantizations of Nakajima quiver varieties associated to bouquet quivers. We show that there are no finite dimensional representations of the quan…

math.GT2018

Nontrivial Topological Quandles

Boris Tsvelikhovskiy

We show that there are infinitely many nonisomorphic quandle structures on any topogical space $X$ of positive dimension. In particular, we disprove the conjecture, asserting that…

Notes from a family of smooth G-Hilbert schemes

On a Dichotomy for Skyscraper Sheaves under the Bridgeland-King-Reid Equivalence

On Poincare polynomials of shuffle algebra representations

On categories O of quiver varieties overlying the bouquet graphs

Nontrivial Topological Quandles

Notes from a family of smooth $G$ -Hilbert schemes

On categories $O$ of quiver varieties overlying the bouquet graphs