# Obstructions to Deforming Space Curves and Non-reduced Components of the Hilbert Scheme

### Hirokazu Nasu

Kyoto University, Japan

## Abstract

Let *H_ℙ3_S* denote the Hilbert scheme of smooth connected curves in ℙ3. We consider maximal irreducible closed subsets *W* ⊂ *H_ℙ3_S* whose general member *C* is contained in a smooth cubic surface and investigate the conditions for *W* to be a S component of (*H_ℙ3_S*)red. We especially study the case where the dimension of the S tangent space of *H_ℙ3_S* at [*C*] is greater than dim *W* (≥ 4 deg(*C*)) by one. We compute obstructions to deforming *C* in ℙ3 and prove that for every *W* in this case, *H_ℙ3_S* is non-reduced along *W* and *W* is a component of (*H_ℙ3_S*)red.

## Cite this article

Hirokazu Nasu, Obstructions to Deforming Space Curves and Non-reduced Components of the Hilbert Scheme. Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, pp. 117–141

DOI 10.2977/PRIMS/1166642061