Integral cohomology of Hilbert schemes of points on surfaces
The purpose of this paper is to settle a conjecture raised by \textit{Z. Qin} and \textit{W. Wang} in their paper ``Integral operators and integral cohomology classes of Hilbert schemes'' [Math. Ann. 331, No. 3, 669--692 (2005; Zbl 1081.14006)]. The conjecture states that, under a particular hypothesis, certain homological operators are integral. To this end the authors use topological \(K\)-theory and the algebra of rings of symmetric functions. The result is then used to obtain explicit generators for the integral cohomology of the Hilbert scheme of \(n\) points on a smooth projective surface which has no odd cohomology. The paper is well written, thorough and contains the necessary information on Hilbert schemes of points on surfaces. Several computations are worked out explicitly.
scientific article; zbMATH DE number 5543231