A remark on the Hilbert scheme of smooth complex space curves

1991 ◽  
Vol 71 (1) ◽  
pp. 307-316 ◽  
Author(s):  
Changho Keem
Keyword(s):  
Hilbert Scheme ◽  
Complex Space ◽  
Space Curves ◽  
Smooth Complex

scholarly journals The integral cohomology of the Hilbert scheme of points on a surface

2020 ◽  
Vol 8 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Natural Number ◽  
Hilbert Scheme ◽  
Obstruction Theory ◽  
Projective Surface ◽  
Hilbert Schemes ◽  
Complex Projective Surface ◽  
Smooth Complex ◽  
Hilbert Scheme Of Points ◽  
Complex Projective ◽  
Torsion Free

Abstract We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme $X^{[n]}$ has torsion-free cohomology for every natural number n. This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas’s reduced obstruction theory for nested Hilbert schemes of surfaces.

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.

EQUISINGULARITY AND LAGRANGEAN CURVES

2001 ◽  
Vol 33 (5) ◽  
pp. 527-534
Author(s):  
ORLANDO NETO
Keyword(s):  
Symplectic Manifold ◽  
Complex Space ◽  
Space Curves ◽  
Definition Of

The most natural candidates to the definition of equisingularity of germs of complex space curves are discussed, showing that they coincide in the case of Lagrangean curves (projectivizations of conic Lagrangean varieties of a symplectic manifold of dimension four).

scholarly journals A global morphism from the Douady space to the cycle space

2007 ◽  
Vol 101 (1) ◽  
pp. 19 ◽  
Author(s):  
Jón Ingólfur Magnússon
Keyword(s):  
Hilbert Scheme ◽  
Complex Space ◽  
Cycle Space

We establish, for any given complex space $M$, a global morphism from the reduction of its Douady space to its cycle space. This morphism is an extension of the morphism defined in [1] from the subspace of the Douady space formed by all pure dimensional subspaces of $M$ to the cycle space of $M$. In the case where $M$ is projective this morphism is the classical morphism from the Hilbert scheme of $M$ to the Chow scheme of $M$.

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
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