Skip to main content

Mirror property for nonsingular mixed configurations of one line and k points in R3

Other Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1524)

Abstract

Given h,k≥0, M(h,k) denotes the set of nonsingular mixed configurations of h lines and k points in ℝ3. We will say that f∈M(h,k) is mirror if it is isotopic to its mirror image in any plane. The following problem has been proposed by Viro and Drobotukhina [3]: given h,k≥0, does there exist some mirror configuration on M(h,k)? A satisfactory answer is given when h=1: f∈M(1,k) is mirror if and only if k≤3.

1980 Mathematics Subject Classification

  • Primary 51A20

Partially suported by DGICYT PB89-0201

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. V. M. Kharlamov, Non-amphicheiral surfaces of degree 4 in ℝP3, Topology and Geometry (Rokhlin Seminar), Lecture Notes in Math., vol.1346, Springer, 1988, pp. 349–356.

    CrossRef  MathSciNet  Google Scholar 

  2. O. Ya. Viro, Topological problems concerning lines and points of three-dimensional space, Soviet Math. Dokl. 32 (1985), no.2, pp. 528–531.

    MathSciNet  MATH  Google Scholar 

  3. O. Ya. Viro and Yu. V. Drobotukhina, Configurations of skew lines, Leningrad Math. J. 1 (1990), no.4, pp. 1027–1050.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Borobia, A. (1992). Mirror property for nonsingular mixed configurations of one line and k points in R3 . In: Coste, M., Mahé, L., Roy, MF. (eds) Real Algebraic Geometry. Lecture Notes in Mathematics, vol 1524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084614

Download citation

  • DOI: https://doi.org/10.1007/BFb0084614

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55992-4

  • Online ISBN: 978-3-540-47337-4

  • eBook Packages: Springer Book Archive