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arXiv · 1708.06325

Segre classes of tautological bundles on Hilbert schemes of surfaces

Claire Voisin
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Abstract

We first give an alternative proof, based on a simple geometric argument, of a result of Marian, Oprea and Pandharipande on top Segre classes of the tautological bundles on Hilbert schemes of $K3$ surfaces equipped with a line bundle. We then turn to the blow-up of $K3$ surface at one point and establish vanishing results for the corresponding top Segre classes in a certain range. This determines, at least theoretically, all top Segre classes of tautological bundles for any pair $(\Sigma,H),\,H\in {\rm Pic}\,\Sigma$.

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Claire Voisin. 2017-08-21. Segre classes of tautological bundles on Hilbert schemes of surfaces. https://arxiv.org/abs/1708.06325

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