ℓ-away ACM line bundles on a nonsingular cubic surface

2024/08/08 by Bhattacharya, Debojyoti, Parameswaran, A. J., Pine, Jagadish
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.04464

Abstract

Let X ⊂ \mathbb P³ be a nonsingular cubic hypersurface. Faenzi (\citeF) and later Pons-Llopis and Tonini (\citePLT) have completely characterized ACM line bundles over X. As a natural continuation of their study in the non-ACM direction, in this paper, we completely classify ℓ-away ACM line bundles (introduced recently by Gawron and Genc (\citeGG)) over X, when ℓ ≤ 2. For ℓ≥ 3, we give examples of ℓ-away ACM line bundles on X and for each ℓ ≥ 1, we establish the existence of smooth hypersurfaces X^(d) of degree d >ℓ in \mathbb P³ admitting ℓ-away ACM line bundles.

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