Obstructions to deforming curves on a 3 - fold , I — a generalization of Mumford ’ s example and an application to Hom schemes — Shigeru Mukai ∗ and
نویسندگان
چکیده
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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Obstructions to deforming curves on a 3-fold, II: Deformations of degenerate curves on a del Pezzo 3-fold
We study the Hilbert scheme Hilb V of smooth connected curves on a smooth del Pezzo 3-fold V . We prove that every degenerate curve C, i.e. every curve contained in a smooth hyperplane section S of V , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) χ(V, IC(S)) ≥ 1 and (ii) for every line ` on S such that ` ∩ C = ∅, the normal bundle N`/V is trivial ...
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