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arXiv · 2106.01991

Very free rational curves in Fano varieties

Izzet Coskun·Geoffrey Smith
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Abstract

Let $X$ be a projective variety and let $C$ be a rational normal curve on $X$. We compute the normal bundle of $C$ in a general complete intersection of hypersurfaces of sufficiently large degree in $X$. As a result, we establish the separable rational connectedness of a large class of varieties, including general Fano complete intersections of hypersurfaces of degree at least three in flag varieties, in arbitrary characteristic. In addition, we give a new way of computing the normal bundle of certain rational curves in products of varieties in terms of their restricted tangent bundles and normal bundles on each factor.

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Izzet Coskun, Geoffrey Smith. 2021-06-03. Very free rational curves in Fano varieties. https://arxiv.org/abs/2106.01991

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