A. Oblomkov

activity

20022026

most citedThe Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link

128 citations · 414 across the 40 of their papers we have counts for

collaborators

44 papers

math.AG2026

Quot scheme of points on torus knot singularities

Yifeng Huang, Ruofan Jiang, Alexei Oblomkov

For $g cd (a, b) = 1$ , we show that the moduli space of $m$ -codimensional $k [[T^{a}, T^{b}]]$ -submodules of $k [[T]]^{n}$ is paved by affine cells, by proving that each Białyni…

math.AG2026

Wall-crossing for Hilbert schemes

Ian Cavey, Eugene Gorsky, Alexei Oblomkov +1

The goal of the minimal model program for the Hilbert scheme of points on a surface aims is to describe the (stable) base loci of all divisors, their associated birational models,…

math.RT2025

A categorification of representations of $U_{q} (gl_{1∣1})$

Alexei Oblomkov, Lev Rozansky

We categorify the action of $U_{q} (gl_{1∣1})$ on the tensor product of its vector representations $(C^{1∣1})^{\otimes N}$ . The generators $E$ and $F$ are represen…

math.AG2025

Newton-Okounkov bodies for nested Hilbert schemes

Ian Cavey, Eugene Gorsky, Alexei Oblomkov +1

We study sections of line bundles on the nested Hilbert scheme of points on the affine plane. We describe the spaces of sections in terms of certain ideals introduced by Haiman, an…

math.AG2025

Discriminants and motivic integration

Oscar Kivinen, Alexei Oblomkov, Dimitri Wyss

We study invariants of a plane cuve singularity $(f, 0)$ coming from motivic integration on symmetric powers of a formal deformation of $f$ . We show that a natural discriminant inte…

math.AG2023

Fixed loci of symplectic automorphisms of $K 3^{[n]}$ and $n$ -Kummer type manifolds

Ljudmila Kamenova, Giovanni Mongardi, Alexei Oblomkov

The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces…