Skip to Main content Skip to Navigation

On the geometry of polar varieties

Abstract : We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are necessary to prove the correctness and complexity estimates of these algorithms. Our results form also the geometrical main ingredients for the computational treatment of singular hypersurfaces. In particular, we show the non–emptiness of suitable generic dual polar varieties of (possibly singular) real varieties, show that generic polar varieties may become singular at smooth points of the original variety and exhibit a sufficient criterion when this is not the case. Further, we introduce the new concept of meagerly generic polar varieties and give a degree estimate for them in terms of the degrees of generic polar varieties. The statements are illustrated by examples and a computer experiment.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01148162
Contributor : Lip6 Publications <>
Submitted on : Monday, May 4, 2015 - 10:58:24 AM
Last modification on : Thursday, March 5, 2020 - 6:36:15 PM

Links full text

Identifiers

Citation

Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din, Éric Schost. On the geometry of polar varieties. Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 2010, 21 (1), pp.33--83. ⟨10.1007/s00200-009-0117-1⟩. ⟨hal-01148162⟩

Share

Metrics

Record views

222