Euler characteristics of Hilbert schemes of points on simple surface singularities

Gyenge, Ádám; Némethi, András; Szendrői, Balázs

doi:10.1007/s40879-018-0222-4

Cited by 21 publications

(31 citation statements)

References 37 publications

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“…In this version, we have updated the bibliography and added references [6,14,15,16,53] in order to reflect some recent developments in the subject. We briefly comment on them.…”

Section: Note Added In 2017mentioning

confidence: 99%

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A Combinatorial Study on Quiver Varieties

Fujii¹,

Minabe²

2017

SIGMA

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Abstract. This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincaré polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young diagrams. In the second part, we give a brief survey of instanton counting in physics, where quiver varieties appear as moduli spaces of instantons, focusing on its combinatorial aspects.

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“…In this version, we have updated the bibliography and added references [6,14,15,16,53] in order to reflect some recent developments in the subject. We briefly comment on them.…”

Section: Note Added In 2017mentioning

confidence: 99%

“…cit. is used in [14,16] to compute the generating functions of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D.…”

Section: Note Added In 2017mentioning

confidence: 99%

A Combinatorial Study on Quiver Varieties

Fujii¹,

Minabe²

2017

SIGMA

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“…From a representation-theoretic point of view, the formulas (3)-(4) compute the character of the basic representation of this Lie algebra, compatibly with the Frenkel-Kac construction. For details from the present point of view, see [18,Section 4 and Appendix A]. For the special case r = 1, gl 1 is just the infinite dimensional Heisenberg algebra, acting on its standard (fermionic) Fock space representation.…”

Section: 2mentioning

confidence: 99%

“…Proof. The proof works along the same lines as the proof of Theorem 2.1; details are spelled out in [18].…”

Section: (R)mentioning

confidence: 99%

Enumerating coloured partitions in 2 and 3 dimensions

Davison¹,

Ongaro²,

Szendrői³

2019

Math. Proc. Camb. Phil. Soc.

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We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a conjecture concerning a factorisation property of the generating function of coloured plane partitions that can be thought of as an orbifold analogue of a conjecture of Maulik et al., now a theorem, in three-dimensional Donaldson-Thomas theory. We study natural quantisations of the generating functions arising from geometry, discuss a quantised version of our conjecture, and prove a positivity result for the quantised coloured plane partition function under a geometric assumption.

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“…A study of the Hilbert zeta function for singular surfaces is a natural next step in view of the results here, and first steps in this direction are taken in [10]. A more concrete goal would be to establish rationality for generically non-reduced curves, where our explicit methods do not seem to generalize in a straightforward way.…”

Section: Introductionmentioning

confidence: 99%