The maximal genus of space curves in the range A

2018/11/21 by Edoardo Ballico, Ballico, Edoardo, Philippe Ellia +1
Mathematics · #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1811.08807

Abstract

Fix positive integers d;m such that (m²+4m+6)/6 ≤ d < (m²+4m+6)/3 (the so-called Range A for space curves). Let G(d;m) be the maximal genus of a smooth and connected curve, of degree d, C ⊂ P³ such that h⁰(I_C(m-1)) = 0. Here we prove that G(d,m) = 1+(m-1)d -\binomm+23 if m≥ 13.8⋅ 10⁵.

Related

• On plane maximal curves
• Maximal rank of space curves in the range A
• Curves of maximal genus in P⁵
• The maximum genus problem for locally Cohen-Macaulay space curves
• The Maximal Rank Conjecture