Duality of planar and spacial curves: new insight
Algebraic Geometry
2015-06-29 v3
Abstract
We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use of duality transformation leads to a series of new sufficient conditions for a regular behavior of the equiclassical stratification. We also discuss duality of curves in higher-dimensional projective spaces and in Grassmannians with focus on similar questions of the regularity of equiclassical families of spacial curves.
Keywords
Cite
@article{arxiv.1412.1944,
title = {Duality of planar and spacial curves: new insight},
author = {Victor Kulikov and Eugenii Shustin},
journal= {arXiv preprint arXiv:1412.1944},
year = {2015}
}
Comments
22 pages; slightly edited according to the referee suggestions; to appear in European Journal of Mathematics