Integral operators and integral cohomology classes of Hilbert schemes

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The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and conjecturally, for all simply connected surfaces).
LaTex, 21 pages, added a new subsection and remark, other minor modifications, to appear in Math. Ann

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