• 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
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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