scholarly journals Hilbert scheme of smooth space curves

1986 ◽  
Vol 19 (4) ◽  
pp. 469-478 ◽  
Author(s):  
Lawrence Ein
Keyword(s):  
Hilbert Scheme ◽  
Space Curves ◽  
Smooth Space

ON THE NUMBER OF IRREDUCIBLE COMPONENTS OF THE HILBERT SCHEME OF SMOOTH SPACE CURVES

1992 ◽  
Vol 03 (06) ◽  
pp. 799-807 ◽  
Author(s):  
PHILIPPE ELLIA ◽  
ANDRÉ HIRSCHOWITZ ◽  
EMILIA MEZZETTI
Keyword(s):  
Hilbert Scheme ◽  
Space Curves ◽  
Irreducible Components ◽  
Smooth Space

scholarly journals Components of the Hilbert scheme of space curves on low-degree smooth surfaces

2015 ◽  
Vol 26 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Jan O. Kleppe ◽  
John C. Ottem
Keyword(s):  
Hilbert Scheme ◽  
Smooth Surface ◽  
Plane Curve ◽  
Picard Number ◽  
Connected Space ◽  
Space Curves ◽  
Cubic Surfaces ◽  
Smooth Component ◽  
Low Degree ◽  
Smooth Plane

We study maximal families W of the Hilbert scheme, H(d, g)sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of H(d, g)sc and we determine dim W. If s = 4 and W is an irreducible component of H(d, g)sc, then the Picard number of S is at most 2 and we explicitly describe, also for s ≥ 5, non-reduced and generically smooth components in the case Pic (S) is generated by the classes of a line and a smooth plane curve of degree s - 1. For curves on smooth cubic surfaces the first author finds new classes of non-reduced components of H(d, g)sc, thus making progress in proving a conjecture for such families.

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