Abstract:
The additive basis of the rational cohomology of the Hilbert schemes of points of surfaces can be found based upon the work of Gottsche, Growjnowski and Nakajima.The ring generators for rational cohomology were found by Qin, Wang and Li via the vertex algebraic calculus method developed by Lehn and Sorger, Qin, Wang and Li. Using the decomposition of the diagonal of the Hilbert scheme, Ellingsrud and Stromme, Beauville, and Markman found the integral ring generators for surfaces with negative canonical divisor and K3. For a general surface, Qin and Wang found a method of intergral operators to study the integral cohomology. In this lecture, we will talk about the application of the methods mentioned above to the additive integral basis and integral ring generators for the cohomology of the Hilbert schemes of points on simply-connected surfaces.
