Let M be a five-dimensional manifold polarized by a very ample line bundle L. We show that a smooth A in the linear system defined by L cannot be a holomorphic $P^1$-bundle over a smooth projective 3-fold Y, unless Y is isomorphic to $P^3$ and A is isomorphic to $P^1 x P^3$.

A note on $P^1$-bundles as hyperplane sections

FANIA, Maria Lucia;
2005-01-01

Abstract

Let M be a five-dimensional manifold polarized by a very ample line bundle L. We show that a smooth A in the linear system defined by L cannot be a holomorphic $P^1$-bundle over a smooth projective 3-fold Y, unless Y is isomorphic to $P^3$ and A is isomorphic to $P^1 x P^3$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18809
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