Grassmannians of secant varieties

2000/05/22 by Luca Chiantini, L. Chiantini, Marc Coppens +3 · 2 citations
Agricultural and Biological Sciences · Mathematics · Medicine · #Phytoestrogen effects and research #Sesame and Sesamin Research #Tensor decomposition and applications #math.AG #msc:14N05

paper · pdf · doi:10.48550/arxiv.math/0005202

AMS-TeX with amsppt style, 12 pages

arxiv created 2000/05/22 · arxiv updated 2009/11/30

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 P⁵.

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