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 Moduli of Space Sheaves with Hilbert Polynomial 4m+ 1

2018 ◽  
Vol 61 (2) ◽  
pp. 328-345 ◽  
Author(s):  
Mario Maican
Keyword(s):  
Euler Characteristic ◽  
Moduli Space ◽  
Elementary Proof ◽  
Hilbert Polynomial ◽  
Space Curves ◽  
Irreducible Components

AbstractWe investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

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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