Singularities of secant maps of immersed surfaces

Author: Ghosh Sunayana   Rieger Joachim  

Publisher: Springer Publishing Company

ISSN: 0046-5755

Source: Geometriae Dedicata, Vol.121, Iss.1, 2006-08, pp. : 73-87

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Abstract

The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion at the diagonal in the source is a stable map-germ in the following cases: (i) c≥ 2 and (2n,n + c − 1) is a pair of dimensions for which the stable germs of rank at least n are dense, and (ii) for generically immersed surfaces (i.e., n = 2 and any c≥ 1). In the latter surface case the -classification of germs of secant maps at the diagonal is described and it is related to the -classification of certain singular projections of the surfaces.