Singularities of the Hilbert scheme of effective divisors
Fecha
2017-01-10Metadatos
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In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic
not extensively studied. We prove that there exists such effective divisors $D$ satisfying
the property: there exists infinitesimal deformations of $D$ not deforming the associated reduced scheme $D_{\mathrm{red}}$.
We observe that such infinitesimal deformations contribute to non-reducedness of the corresponding
Hilbert scheme. We finally introduce a concept of simple extension of curves and notice that the above
mentioned property is preserved under simple extension of curves.