We give a completely different, much shorter, proof of a substantial generalization of the main result from \cite{KS}. It states that embedded projective $n$-folds swept out by quadrics of dimension at least $\big[\frac n2\big] +2$ are either scrolls or hyperquadric fibrations, which are also Mori contractions.
On manifolds swept out by high dimensional quadrics
BELTRAMETTI, MAURO CARLO;
2008-01-01
Abstract
We give a completely different, much shorter, proof of a substantial generalization of the main result from \cite{KS}. It states that embedded projective $n$-folds swept out by quadrics of dimension at least $\big[\frac n2\big] +2$ are either scrolls or hyperquadric fibrations, which are also Mori contractions.
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