On codimension two subvarieties of P6

1999/09/23 by Philippe Ellia, Ellia, Philippe, Davide Franco +1 · 1 citation
Mathematics · #14J60 #14J99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14J60 #msc:14J99

paper · pdf · doi:10.48550/arxiv.math/9909137

23 pages (Latex)

arxiv created 1999/09/23 · openalex publication_date 1999/09/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following: (a) Let X be a smooth, codimension two subvariety of P6. If X lies on a hyperquintic or if deg(X)<74, then X is a complete intersection. (b) Let X be a smooth, subcanonical threefold in P5. If X lies on a hyperquartic, then X is a complete intersection.

Cited by

• On subcanonical surfaces of P⁴

Related

• On a special class of smooth codimension two subvarieties in ℙⁿ, n ≥ 5
• On codimension-two subcanonical varieties inside ℙⁿ
• Subvarieties of small codimension in smooth projective varieties
• Criteria for complete intersections
• Gherardelli linkage and complete intersections