# A support theorem for Hilbert schemes of planar curves

@article{Migliorini2013AST,
title={A support theorem for Hilbert schemes of planar curves},
author={L. Migliorini and V. Shende},
journal={Journal of the European Mathematical Society},
year={2013},
volume={15},
pages={2353-2367}
}
• Published 2013
• Mathematics
• Journal of the European Mathematical Society
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve… Expand
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