Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 078, 16 pages      arXiv:2201.07392      https://doi.org/10.3842/SIGMA.2022.078
Contribution to the Special Issue on Enumerative and Gauge-Theoretic Invariants in honor of Lothar Göttsche on the occasion of his 60th birthday

K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces

Noah Arbesfeld
Department of Mathematics, Huxley Building, Imperial College London, London SW7 2AZ, UK

Received January 28, 2022, in final form October 03, 2022; Published online October 16, 2022

Abstract
We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendent series. Our approach is to control equivariant holomorphic Euler characteristics over the Hilbert scheme of points on the affine plane. To do so, we slightly modify a Macdonald polynomial identity of Mellit.

Key words: Hilbert schemes; tautological bundles; Macdonald polynomials.

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