Codimension 2 subvarieties of projective space
Hartshorne conjectures that if Y is a smooth projective variety of codimension 2 in \({\mathbb{P}}^ n (n\geq 6)\), then Y is a complete intersection. Let E be a rank 2 bundle on projective n-space and X be a codimension 2 zero-scheme of a section of E. Using a construction of Ran, the author studies the secant variety of X. He concludes that X is a complete intersection under various numerical assumptions on X. He also studies unstable rank 2 bundles and numerically split bundles.
scientific article; zbMATH DE number 4179547