Consider a family of integral complex locally planar curves. We show that under some assumptions on the base, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem of Beilinson, Bernstein and Deligne asserts that the pushforward of the constant sheaf on the relative nested Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension.

A support theorem for nested Hilbert schemes of planar curves / Felisetti, Camilla. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 164:(2021), pp. 467-488. [10.1007/s00229-020-01189-z]

A support theorem for nested Hilbert schemes of planar curves

Felisetti, Camilla
2021-01-01

Abstract

Consider a family of integral complex locally planar curves. We show that under some assumptions on the base, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem of Beilinson, Bernstein and Deligne asserts that the pushforward of the constant sheaf on the relative nested Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension.
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A support theorem for nested Hilbert schemes of planar curves / Felisetti, Camilla. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 164:(2021), pp. 467-488. [10.1007/s00229-020-01189-z]
Felisetti, Camilla
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1286090
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