Ideals of the Cohomology Rings of Hilbert Schemes and Their Applications
نویسندگان
چکیده
We study the ideals of the rational cohomology ring of the Hilbert scheme X [n] of n points on a smooth projective surface X . As an application, for a large class of smooth quasi-projective surfaces X , we show that every cup product structure constant of H∗(X ) is independent of n; moreover, we obtain two sets of ring generators for the cohomology ring H∗(X ). Similar results are established for the Chen-Ruan orbifold cohomology ring of the symmetric product. In particular, we prove a ring isomorphism between H∗(X ;C) and H∗ orb(X n/Sn;C) for a large class of smooth quasi-projective surfaces with numerically trivial canonical class.
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