Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford's example and an application to Hom schemes

Abstract

We give a sufficient condition for a first order infinitesimal deformation of a curve on a 3-fold to be obstructed. As application we construct generically non-reduced components of the Hilbert schemes of uniruled 3-folds and the Hom scheme from a general curve of genus five to a general cubic 3-fold.

v2: 19 pages, Theorem 1.3 improved, minor errors and typos corrected, a reference added

Cited by in corpus (3)

• Obstructions to deforming curves on a 3-fold, III: Deformations of curves lying on a K3 surface
• The Hilbert scheme of space curves sitting on a smooth surface containing a line
• Components of the Hilbert scheme of space curves on low-degree smooth surfaces