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arXiv · 1505.06488

On Varieties of Lines on Linear Sections of Grassmannians

Rafael Lucas de Arruda
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Abstract

General linear sections of codimension 2 of the Grassmannians G(1,4) and G(1,5) appear in the classification of Fano manifolds of high index. Unlike Grassmannians, these manifolds are not homogeneous. Nevertheless, their automorphisms groups have finitely many orbits. In this work we first compute the orbits of these actions. Then we give a description of the variety of lines (under the Plücker embedding) passing through a fixed point in each orbit of the action. As an application we show that these Fano manifolds are not weakly 2-Fano, completing the classification of weakly 2-Fano manifolds of high index, initiated by Carolina Araujo and Ana-Maria Castravet.

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Rafael Lucas de Arruda. 2015-05-24. On Varieties of Lines on Linear Sections of Grassmannians. https://arxiv.org/abs/1505.06488

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