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Some properties of Fano manifolds that are zeros of sections in homogenous vector bundles over Grassmannians

Oliver Küchle
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Abstract

Let $X$ be a Fano manifold which is the zero scheme of a general global section $s$ in an irreducible homogenous vector bundle over a Grassmannian. We prove that the restriction of the Plücker embedding embeds $X$ projectively normal, and that every small deformation of $X$ comes from a deformation of the section $s$. These results are strengthened in the case of Fano 4-folds.

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BibTeXRIS

Oliver Küchle. 1994-05-20. Some properties of Fano manifolds that are zeros of sections in homogenous vector bundles over Grassmannians. https://arxiv.org/abs/alg-geom/9405009

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