Geodesic
Flags of sheaves, quivers and symmetric polynomials
Forum of Mathematics, Sigma, Tome 12 (2024)

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We study a quiver description of the nested Hilbert scheme of points on the affine plane and its higher rank generalization – that is, the moduli space of flags of framed torsion-free sheaves on the projective plane. We show that stable representations of the quiver provide an ADHM-like construction for such moduli spaces. We introduce a natural torus action and use equivariant localization to compute some of their (virtual) topological invariants, including the case of compact toric surfaces. We conjecture that the generating function of holomorphic Euler characteristics for rank one is given in terms of polynomials in the equivariant weights, which, for specific numerical types, coincide with (modified) Macdonald polynomials. From the physics viewpoint, the quivers we study describe a class of surface defects in four-dimensional supersymmetric gauge theories in terms of nested instantons. 
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     title = {Flags of sheaves, quivers and symmetric polynomials},
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Giulio Bonelli; Nadir Fasola; Alessandro Tanzini. Flags of sheaves, quivers and symmetric polynomials. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.43

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