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A support theorem for Hilbert schemes of planar curves, II

Published online by Cambridge University Press:  28 April 2021

Luca Migliorini
Affiliation:
Department of Mathematics, Università di Bologna, 40126Bologna, [email protected]
Vivek Shende
Affiliation:
Department of Mathematics, University of California, Berkeley, CA94720, [email protected]
Filippo Viviani
Affiliation:
Department of Mathematics, Università di Roma Tre, 00146Roma, [email protected]

Abstract

We study the cohomology of Jacobians and Hilbert schemes of points on reduced and locally planar curves, which are however allowed to be singular and reducible. We show that the cohomologies of all Hilbert schemes of all subcurves are encoded in the cohomologies of the fine compactified Jacobians of connected subcurves, via the perverse Leray filtration. We also prove, along the way, a result of independent interest, giving sufficient conditions for smoothness of the total space of the relative compactified Jacobian of a family of locally planar curves.

Type
Research Article
Copyright
© The Author(s) 2021

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Footnotes

L.M. is partially supported by PRIN project 2015 ‘Spazi di moduli e teoria di Lie’. During the (long) preparation of this paper L.M. was a member of the School of Mathematics of the Institute for Advanced Study in Princeton, partially funded by the Giorgio and Elena Petronio fellowship. V. S. is supported by the NSF grant DMS-1406871, and by a Sloan fellowship. F.V. is partially supported by PRIN ‘Geometria delle varietà algebriche’ and GNSAGA-INdAM.

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