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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 078, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.078 (Mi sigma1874) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2022.078
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.
Funding agency Grant number
Engineering and Physical Sciences Research Council EP/R013349/1
National Science Foundation DMS-1902717
This work was supported by the EPSRC through grant EP/R013349/1 and the NSF through grant DMS-1902717.
Received: January 28, 2022; in final form October 3, 2022; Published online October 16, 2022
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Document Type: Article
MSC: 14C05, 14C17, 05E05
Language: English
Citation: Noah Arbesfeld, “K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces”, SIGMA, 18 (2022), 078, 16 pp.
Citation in format AMSBIB
\Bibitem{Arb22}
\by Noah~Arbesfeld
\paper K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces
\jour SIGMA
\yr 2022
\vol 18
\papernumber 078
\totalpages 16
\mathnet{http://mi.mathnet.ru/sigma1874}
\crossref{https://doi.org/10.3842/SIGMA.2022.078}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4496136}
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