Codice  QDD 141 
Titolo  Smooth curves specialize to extremal curves 
Data  20121115 
Autore/i  Hartshorne, R.; Lella, P.; Schlesinger, E: 
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Abstract  Let H_{d,g} denote the Hilbert scheme of locally CohenMacaulay curves of degree d and genus g in projective three space. We show that, given a smooth irreducible curve C of degree d and genus g, there is a rational curve {[C_t]} in H_{d,g} such that C_t for t neq 0 is projectively equivalent to C, while the special fibre C_0 is an extremal curve. It follows that smooth curves lie in a unique connected component of H_{d,g}. We also determine necessary and sufficient conditions for a locally CohenMacaulay curve to admit such a specialization to an extremal curve. 
