2025/11/25 by Manoj Kummini, Kummini, Manoj, Subramanian, Abhiram
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2511.19962
Let X ⊆ ℙn, n ≥ 4 be a codimension-two subcanonical local complete intersection variety with ideal sheaf IX. Let aX ∈ ℤ be such that ωX = \mathscrOX(aX). Assume that there exists j ≤ (aX+n+2)/(2) such that Γ(IX(j)) ≠ 0. We prove some sufficient conditions on the first deficiency module H1_*(IX) that ensures that X is a complete intersection. We also show that smooth codimension-two 3-Buchsbaum varieties inside ℙn, n ≥ 6 are complete intersections.