JournalsjemsVol. 24, No. 8pp. 2979–3015

Higher rank Segre integrals over the Hilbert scheme of points

  • Alina Marian

    Northeastern University, Boston, USA
  • Dragos Oprea

    University of California San Diego, La Jolla, USA
  • Rahul Pandharipande

    ETH Zürich, Switzerland
Higher rank Segre integrals over the Hilbert scheme of points cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

Let SS be a nonsingular projective surface. Each vector bundle VV on SS of rank ss induces a tautological vector bundle over the Hilbert scheme of nn points of SS. When s=1s=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 the tautological bundles for all ranks ss over all KK-trivial surfaces. Furthermore, in rank s=2s=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.

Cite this article

Alina Marian, Dragos Oprea, Rahul Pandharipande, Higher rank Segre integrals over the Hilbert scheme of points. J. Eur. Math. Soc. 24 (2022), no. 8, pp. 2979–3015

DOI 10.4171/JEMS/1149