On codimension two subvarieties in hypersurfaces

N. Mohan Kumar, A. P. Rao, G. V. Ravindra

Published 2010-05-21Version 1

We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two subvariety $S\subset\bbP^n$. We also show there exist $Y\subset X$ as above for which the normal bundle sequence for the inclusion $Y\subset X\subset\bbP^n$ does not split.