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

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

2006-09-11

arxiv.org/abs/math/0609284v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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