Generating series in the cohomology of Hilbert schemes of points on surfaces
Samuel Boissière and Marc A. Nieper-Wisskirchen
Abstract: In the study of the rational cohomology of Hilbert schemes of
points on a smooth surface, it is particularly interesting to
understand the characteristic classes of the tautological bundles
and the tangent bundle. The authors of this note pursue this
study. They first collect all results appearing separately in the
literature, and prove some new formulas using Ohmoto's results on
orbifold Chern classes on Hilbert schemes. They also explain the
algorithmic counterpart of the topic: the cohomology space is
governed by a vertex algebra that can be used to compute
characteristic classes. They present an implementation of the
vertex operators in the rewriting logic system
MAUDE, and address observations and conjectures
obtained after symbolic computations.
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