Mathematics – Algebraic Geometry
Scientific paper
2001-12-07
Contemp. Math. 310 (2002), 233--257.
Mathematics
Algebraic Geometry
26 pages, latex, main changes: the sign convention in the definition of $J^p_n(\alpha)$ in sect. 4.5 is modified and it leads
Scientific paper
Given a closed complex manifold $X$ of even dimension, we develop a systematic (vertex) algebraic approach to study the rational orbifold cohomology rings $\orbsym$ of the symmetric products. We present constructions and establish results on the rings $\orbsym$ including two sets of ring generators, universality and stability, as well as connections with vertex operators and W algebras. These are independent of but parallel to the main results on the cohomology rings of the Hilbert schemes of points on surfaces as developed in our earlier works joint with W.-P. Li. We introduce a deformation of the orbifold cup product and explain how it is reflected in terms of modification of vertex operators in the symmetric product case. As a corollary, we obtain a new proof of the isomorphism between the rational cohomology ring of Hilbert schemes and the ring $\orbsym$ (after some modification of signs), when X is a projective surface with a numerically trivial canonical class; we show that no sign modification is needed if both cohomology rings use complex coefficients.
Qin Zhenbo
Wang Weiqiang
No associations
LandOfFree
Hilbert schemes and symmetric products: a dictionary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hilbert schemes and symmetric products: a dictionary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert schemes and symmetric products: a dictionary will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-326161