Lines on projective varieties and applications

Details Lines on projective varieties and applications Lines on projective varieties and applications

2010-09-19

arxiv.org/abs/1009.3637v2

Mathematics

Algebraic Geometry

15 pages. One example removed; one remark and some references added; typos corrected

Scientific paper

10.1007/s12215-011-0072-0

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.

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