A support theorem for Hilbert schemes of planar curves, II

Migliorini Luca; Shende Vivek; Viviani Filippo

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A support theorem for Hilbert schemes of planar curves, II

机译：A support theorem for Hilbert schemes of planar curves, II

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摘要

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.

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《Compositio mathematica》 |2021年第4期|835-882|共48页
作者
Migliorini Luca; Shende Vivek; Viviani Filippo;
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作者单位

Univ Bologna, Dept Math, I-40126 Bologna, Italy;

Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA;

Univ Roma Tre, Dept Math, I-00146 Rome, Italy;

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正文语种英语
中图分类数学;
关键词
compactified Jacobians; Hilbert scheme of points; reduced curves with locally planar singularities; perverse filtration; decomposition theorem; support theorem;

A support theorem for Hilbert schemes of planar curves, II

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