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

DOI10.3842/SIGMA.2022.078arXiv2201.07392MaRDI QIDQ6388605

Publication date: 18 January 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.

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Parametrization (Chow and Hilbert schemes) (14C05) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

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