The Hilbert scheme of space curves sitting on a smooth surface containing a line
arXiv:1801.01101 · doi:10.1007/s12215-016-0266-6
Abstract
We continue the study of maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth degree-s surface S containing a line. For s > 3, we extend the two ranges where W is a unique irreducible (resp. generically smooth) component of H(d,g)_{sc}. In another range, close to the boarder of the nef cone, we describe for s=4 and 5 components W that are non-reduced, leaving open the non-reducedness of only 3 (resp. 2) families for s > 5 (resp. s=5), thus making progress to recent results of Kleppe and Ottem in [28]. For s=3 we slightly extend previous results on a conjecture of non-reduced components, and in addition we show its existence in a subrange of the conjectured range.
arXiv commentThis is a postprint of an article dedicated to Ph. Ellia on his 60'th birthday and published in Rendiconti del Circolo Matematico di Palermo Series 2. The final authenticated version is available online at SpringerLink via the DOI below
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