On the geometry of polar varieties

Details On the geometry of polar varieties On the geometry of polar varieties

2009-10-08

arxiv.org/abs/0910.1476v2

Mathematics

Algebraic Geometry

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the geometry of polar varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the geometry of polar varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the geometry of polar varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-352780