Open AccessSegre classes of tautological bundles on Hilbert schemes of surfaces
Author(s) -
Claire Voisin
Publication year - 2019
Publication title -
algebraic geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.563
H-Index - 20
eISSN - 2214-2584
pISSN - 2313-1691
DOI - 10.14231/ag-2019-010
Subject(s) - argument (complex analysis) , pure mathematics , surface (topology) , hilbert scheme , point (geometry) , bundle , mathematics , simple (philosophy) , line (geometry) , tautological line bundle , theoretical physics , vector bundle , geometry , physics , materials science , normal bundle , biochemistry , chemistry , philosophy , epistemology , frame bundle , composite material
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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