Extendable codimension two subvarieties in a general hypersurface

2025/10/09 by G. V. Ravindra, Debaditya Raychaudhury, Ravindra, G. V. +1
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2510.08108

Abstract

We exhibit a class of extendable codimension 2 subvarieties in a general hypersurface of dimension at least 4 in projective space. As a consequence, we prove that a general hypersurface of degree d and dimension at least 4 does not support globally generated indecomposable ACM bundles of any rank if their first Chern class e ≪ d.

Citations

• Non-existence of low rank Ulrich bundles on Veronese varieties
• Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections
• Restrictions on rational surfaces lying in very general hypersurfaces
• An introduction to Ulrich bundles
• Rank 3 arithmetically Cohen-Macaulay bundles on hypersurfaces
• Splitting of low rank ACM bundles on hypersurfaces of high dimension
• A home-made Hartshorne-Serre correspondence
• Subvarieties of general type on a general projective hypersurface
• Resultants and Chow forms via Exterior Syzygies
• Determinantal hypersurfaces

Related

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• Characterization on projective submanifolds of codimensions 2 and 3
• Subvarieties of low degree on general hypersurfaces
• Subvarieties of Cⁿ with non-extendible Automorphisms
• Infinitesimal extensions of rank two vector bundles on submanifolds of small codimension