Arkiv för Matematik

  • Ark. Mat.
  • Volume 48, Number 1 (2010), 177-206.

Smooth tropical surfaces with infinitely many tropical lines

Magnus Dehli Vigeland

Full-text: Open access

Abstract

We study the tropical lines contained in smooth tropical surfaces in ℝ3. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however, there exist smooth tropical surfaces of any degree with infinitely many tropical lines.

Article information

Source
Ark. Mat., Volume 48, Number 1 (2010), 177-206.

Dates
Received: 15 January 2008
Revised: 13 October 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907098

Digital Object Identifier
doi:10.1007/s11512-009-0116-2

Mathematical Reviews number (MathSciNet)
MR2594592

Zentralblatt MATH identifier
1198.14061

Rights
2009 © Institut Mittag-Leffler

Citation

Vigeland, Magnus Dehli. Smooth tropical surfaces with infinitely many tropical lines. Ark. Mat. 48 (2010), no. 1, 177--206. doi:10.1007/s11512-009-0116-2. https://projecteuclid.org/euclid.afm/1485907098


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