Grassmannians of secant varieties

L. Chiantini; M. Coppens

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Grassmannians of secant varieties

L. Chiantini·M. Coppens

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Abstract

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec_k(X), for 0<h<k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the expected singularities. In particular, we examine the family G of lines sitting in 3-secant planes to a surface S. We show that the actual dimension of G is equal to the expected dimension unless S is a cone or a rational normal scroll of degree 4 in P^5.

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BibTeX RIS

L. Chiantini, M. Coppens. 2000-05-22. Grassmannians of secant varieties. https://arxiv.org/abs/math/0005202

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