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On a special class of smooth codimension two subvarieties in $\mathbb{P}^n$, $n \geq 5$

C. Folegatti
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Abstract

We consider smooth codimension two subcanonical subvarieties in $\mathbb{P}^n$ with $n \geq 5$, lying on a hypersurface of degree $s$ having a linear subspace of multiplicity $(s-2)$. We prove that such varieties are complete intersections. We also give a little improvement to some earlier results on the non existence of rank two vector bundles on $\mathbb{P}^4$ with small Chern classes.

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C. Folegatti. 2004-06-09. On a special class of smooth codimension two subvarieties in $\mathbb{P}^n$, $n \geq 5$. https://arxiv.org/abs/math/0311038

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