Punctual Quot schemes and Cohen--Lenstra series of the cusp singularity

Y Huang, R Jiang - arXiv preprint arXiv:2305.06411, 2023 - arxiv.org
The Quot scheme of points $\mathrm {Quot} _ {d, n}(X) $ on a variety $ X $ over a field $ k $
parametrizes quotient sheaves of $\mathcal {O} _X^{\oplus d} $ of zero-dimensional support …

A geometric interpretation of the Delta Conjecture

M Gillespie, E Gorsky, ST Griffin - arXiv preprint arXiv:2501.00197, 2024 - arxiv.org
We introduce a variety $ Y_ {n, k} $, which we call the\textit {affine $\Delta $-Springer fiber},
generalizing the affine Springer fiber studied by Hikita, whose Borel-Moore homology has …

Generic curves and non-coprime Catalans

E Gorsky, M Mazin, A Oblomkov - arXiv preprint arXiv:2210.12569, 2022 - arxiv.org
We compute the Poincar\'e polynomials of the compactified Jacobians for plane curve
singularities with Puiseaux exponents $(nd, md, md+ 1) $, and relate them to the …

Monotone links in DAHA and EHA

P Galashin, T Lam - arXiv preprint arXiv:2307.16794, 2023 - arxiv.org
We define monotone links on a torus, obtained as projections of curves in the plane whose
coordinates are monotone increasing. Using the work of Morton-Samuelson, to each …

From Cherednik algebras to knot homology via cuspidal D-modules

X Ma - arXiv preprint arXiv:2407.00971, 2024 - arxiv.org
We show that the triply-graded Khovanov-Rozansky homology of the $(m, n) $ torus knot
can be recovered from the finite-dimensional representation $\mathrm {L} _ {m/n} $ of the …