Duality of planar and spacial curves: new insight

Viktor S. Kulikov*, Eugenii Shustin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)462-482
Number of pages21
JournalEuropean Journal of Mathematics
Volume1
Issue number3
DOIs
StatePublished - 1 Sep 2015

Funding

FundersFunder number
National Research University Higher School of Economics, AG Laboratory
German-Israeli Foundation for Scientific Research and Development1174-197.6/2011
Russian Foundation for Basic Research14-01-00160, 15-01-02158
Tel Aviv University
Government Council on Grants, Russian Federation

    Keywords

    • Duality of curves
    • Equiclassical stratification
    • Planar curves
    • Spacial curves

    Fingerprint

    Dive into the research topics of 'Duality of planar and spacial curves: new insight'. Together they form a unique fingerprint.

    Cite this