On the classification of non-aCM curves on quintic hypersurfaces in ℙ³

2022/02/08 by Watanabe, Kenta
#14J29 #14J60 #14J70 #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.03635

Abstract

In this paper, we call a sub-scheme of dimension one in ℙ³ a curve. It is well known that the arithmetic genus and the degree of an aCM curve D in ℙ³ is computed by the h-vector of D. However, for a given curve D in ℙ³, the two invariants of D do not tell us whether D is aCM or not. In this paper, we give a classification of curves on a smooth quintic hypersurface in ℙ³ which are not aCM.

Related

• Algebraic hyperbolicity of the very general quintic surface in ℙ³
• The characterization of aCM line bundles on quintic hypersurfaces in ℙ³
• Classification of genus 3 curves in special strata of the moduli space
• Non hyperelliptic curves of genus three over finite fields of characteristic two
• Geometry of quintics in \mathbb P³ and the Craighero-Gattazzo surface of general type