Tensor products of tautological bundles under the Bridgeland–King–Reid–Haiman equivalence
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We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland–King–Reid–Haiman equivalence. Using this, some new formulas for cohomological invariants of these bundles are obtained. In particular, we give formulas for the Euler characteristic of arbitrary tensor products on the Hilbert scheme of two points and of triple tensor products in general.
KeywordsAlgebraic geometry Hilbert schemes of points Tautological bundles
Mathematics Subject Classification14C05 14F05 14J60
Most of the content of this article is also part of the author’s PhD thesis. The author wants to thank his adviser Marc Nieper-Wißkirchen for his support. The article was finished during the authors stay at the SFB Transregio 45 in Bonn.
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