Higher rank Segre integrals over the Hilbert scheme of points

Alina Marian; Dragos Oprea; Rahul Pandharipande

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arXiv · 1712.02382

Higher rank Segre integrals over the Hilbert scheme of points

Alina Marian·Dragos Oprea·Rahul Pandharipande

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Abstract

Let S be a nonsingular projective surface. Each vector bundle V on S of rank s induces a tautological vector bundle over the Hilbert scheme of n points of S. When s=1, the top Segre classes of the tautological bundles are given by a recently proven formula conjectured in 1999 by M. Lehn. We calculate here the Segre classes of tautological bundles for all ranks s over all K-trivial surfaces. Furthermore, in rank s=2, the Segre integrals are determined for all surfaces, thus establishing a full analogue of Lehn's formula. We also give conjectural formulas for certain series of Verlinde Euler characteristics over the Hilbert schemes of points.

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Alina Marian, Dragos Oprea, Rahul Pandharipande. 2017-12-06. Higher rank Segre integrals over the Hilbert scheme of points. https://arxiv.org/abs/1712.02382

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