Quartic Curves and Their Bitangents

Details Quartic Curves and Their Bitangents Quartic Curves and Their Bitangents

2010-08-24

arxiv.org/abs/1008.4104v2

Journal of Symbolic Computation 46 (2011) 712-733

Mathematics

Algebraic Geometry

26 pages, 3 figures, added references, fixed theorems 4.3 and 7.8, other minor changes

Scientific paper

10.1016/j.jsc.2011.01.007

A smooth quartic curve in the complex projective plane has 36 inequivalent representations as a symmetric determinant of linear forms and 63 representations as a sum of three squares. These correspond to Cayley octads and Steiner complexes respectively. We present exact algorithms for computing these objects from the 28 bitangents. This expresses Vinnikov quartics as spectrahedra and positive quartics as Gram matrices. We explore the geometry of Gram spectrahedra and we find equations for the variety of Cayley octads. Interwoven is an exposition of much of the 19th century theory of plane quartics.

Affiliated with

Also associated with

No associations

Rating

Quartic Curves and Their Bitangents 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 Quartic Curves and Their Bitangents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quartic Curves and Their Bitangents will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-394248