1997•Journal für die reine und angewandte Mathematik (Crelles Journal)Requires access

On codimension-two subvarieties of hypersurfaces.

Ekaterina Amerik

Abstract

Abstract. We show that for a smooth hypersurface X ⊂ Pn of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties Y ⊂ X which are not an intersection X ∩ S for a codimension two subvariety S ⊂ Pn. We also show there exist Y ⊂ X as above for which the normal bundle sequence for the inclusion Y ⊂ X ⊂ Pn does not split. Dedicated to Spencer Bloch

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Key concepts: Subvariety, Codimension, Hypersurface, Mathematics, Pure mathematics, Sequence (biology), Intersection (aeronautics), Combinatorics