• Corpus ID: 202661058

Obstructions to deforming space curves lying on a smooth cubic surface

@article{Nasu2019ObstructionsTD,
  title={Obstructions to deforming space curves lying on a smooth cubic surface},
  author={Hirokazu Nasu},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
  • Hirokazu Nasu
  • Published 18 September 2019
  • Mathematics
  • arXiv: Algebraic Geometry
In this paper, we study the deformations of curves in the projective 3-space $\mathbb P^3$ (space curves), one of the most classically studied objects in algebraic geometry. We prove a conjecture due to J. O. Kleppe (in fact, a version modified by Ph. Ellia) concerning maximal families of space curves lying on a smooth cubic surface, assuming the quadratic normality of its general members. We also give a sufficient condition for curves lying on a cubic surface to be obstructed in $\mathbb P^3… 

References

SHOWING 1-10 OF 25 REFERENCES
Obstructions to deforming curves on a 3-fold, III: Deformations of curves lying on a K3 surface
We study the deformations of a smooth curve $C$ on a smooth projective threefold $V$, assuming the presence of a smooth surface $S$ satisfying $C \subset S \subset V$. Generalizing a result of Mukai
Obstructions to deforming curves on a prime Fano 3‐fold
We prove that for every smooth prime Fano 3‐fold V, the Hilbert scheme HilbscV of smooth connected curves on V contains a generically non‐reduced irreducible component of Mumford type. We also study
Murphy’s law in algebraic geometry: Badly-behaved deformation spaces
We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as
Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford’s example and an application to schemes
We give a sufficient condition for a first order infinitesimal deformation of a curve on a 3-fold to be obstructed. As application we construct generically non-reduced components of the Hilbert
The Hilbert scheme of space curves sitting on a smooth surface containing a line
We continue the study of maximal families W of the Hilbert scheme, $$ {{\mathrm{H}}}(d,g)_{sc}$$H(d,g)sc, of smooth connected space curves whose general curve C lies on a smooth degree-s surface S
Obstructions to deforming curves on an Enriques-Fano 3-fold
Castelnuovo curves and unobstructed deformations
Now it is a well-known fact from Kodai ra [8], that if H i ( N ) = 0 , then there exists a non-singular family ~ for which p is surjective. In classical language, this is the "completeness of the
On generically non‐reduced components of Hilbert schemes of smooth curves
A classical example of Mumford gives a generically non‐reduced component of the Hilbert scheme of smooth curves in P3 such that a general element of the component is contained in a smooth cubic
Le schéma de Hilbert des courbes gauches localement Cohen-Macaulay n'est (presque) jamais réduit
— Let k be an algebraically closed field of characteristic zéro. Let Hd,g dénote thé Hilbert scheme of locally Cohen-Macaulay curves of degree d and genus g contained in thé projective space P|. If d
Components of the Hilbert scheme of space curves on low-degree smooth surfaces
Electronic version of an article published as Kleppe, J. O., & Ottem, J. C. (2015). Components of the Hilbert scheme of space curves on low-degree smooth surfaces. International Journal of
...
1
2
3
...