The genus of curves in \mathbb P⁴ and \mathbb P⁵ not contained in quadrics

2022/03/07 by Vincenzo Di Gennaro, Di Gennaro, Vincenzo
Computer Science · Engineering · Mathematics · #14J26 #14J70 #14M05 #14M06 #14M10 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Primary 14N15 #Secondary 14N25

paper · pdf · doi:10.48550/arxiv.2203.03743

openalex publication_date 2022/03/07 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

A classical problem in the theory of projective curves is the classification of all their possible genera in terms of the degree and the dimension of the space where they are embedded. Fixed integers r,d,s, Castelnuovo-Halphen's theory states a sharp upper bound for the genus of a non-degenerate, reduced and irreducible curve of degree d in \mathbb P^r, under the condition of being not contained in a surface of degree

Related

• A remark on the genus of curves in \mathbf P⁴
• On the genus of projective curves not contained in hypersurfaces of given degree
• On the genus of projective curves not contained in hypersurfaces of given degree, II
• Refining Castelnuovo-Halphen bounds
• The genus of curves on the three dimensional quadric