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

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.

Keywords: Hilbert schemes, tautological bundles, Macdonald polynomials.

MSC: 14C05, 14C17, 05E05

Received: January 28, 2022; in final form October 3, 2022; Published online October 16, 2022

Language: English

DOI: 10.3842/SIGMA.2022.078

Bibliographic databases:

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ArXiv: 2201.07392