Singularities of Tangent Varieties to Curves and Surfaces
Differential Geometry
2012-02-16 v2
Abstract
It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and differential systems on flag manifolds, via several techniques in differentiable algebra. It is provided also the generic diffeomorphism classification of singularities on tangent varieties to contact-integral curves in the standard contact projective space. Moreover we give basic results on the classification of singularities of tangent varieties to generic surfaces and Legendre surfaces.
Keywords
Cite
@article{arxiv.1201.2778,
title = {Singularities of Tangent Varieties to Curves and Surfaces},
author = {Goo Ishikawa},
journal= {arXiv preprint arXiv:1201.2778},
year = {2012}
}
Comments
31pages, 7figures (2nd version, typos are corrected, Arguments for Theorems 7.3 and 9.5 are revised.)