On generically non†reduced components of Hilbert schemes of smooth curves

Ananyo Dan

Mathematische Nachrichten, 2017, vol. 290, issue 17-18, 2800-2814

Abstract: A classical example of Mumford gives a generically non†reduced component of the Hilbert scheme of smooth curves in P3 such that a general element of the component is contained in a smooth cubic surface in P3. In this article we use techniques from Hodge theory to give further examples of such (generically non†reduced) components of Hilbert schemes of smooth curves without any restriction on the degree of the surface containing it. As a byproduct we also obtain generically non†reduced components of certain Hodge loci.

Date: 2017
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https://doi.org/10.1002/mana.201600356

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