Abstract
One of the tantalizing problems in projective geometry is Hartshorne’s conjecture: smooth subvarieties X ⊂ ℙn(ℂ) with dim \(>\frac{2} {3}n \) are complete intersections. Due to Serre’s correspondence the most interesting case is codim X = 2. In fact, in this case even 4-folds in ℙ6 should be complete intersections. For n ≤ 5 the remaining cases of “low codimension” are surfaces in ℙ4 and 3-folds in ℙ5. For surfaces in ℙ4, Ellingsrud and Peskine [8] have established the following beautiful boundedness result.
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Braun, R., Ottaviani, G., Schneider, M., Schreyer, F.O. (1993). Boundedness for Nongeneral-Type 3-Folds in ℙ5 . In: Ancona, V., Silva, A. (eds) Complex Analysis and Geometry. The University Series in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9771-8_13
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DOI: https://doi.org/10.1007/978-1-4757-9771-8_13
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