Obstructions to deforming space curves lying on a smooth cubic surface

2019/09/18 by Nasu, Hirokazu
#14C05 #14D15 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.08452

Abstract

In this paper, we study the deformations of curves in the projective 3-space \mathbb P³ (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 P³ in terms of lines on the surface. For the proofs, we use the Hilbert-flag scheme of \mathbb P³ as a main tool and apply a recent result on primary obstructions to deforming curves on a threefold developed by S. Mukai and the author.

Related

• Obstructions to deforming space curves lying on a del Pezzo surface
• Topological arrangement of curves of degree 6 on cubic surfaces in \Bbb R P³
• Smooth curves on projective K3 surfaces
• Eliminate obstructions: curves on a 3-fold
• Singularities of the Hilbert scheme of non-reduced curves