Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jsc.2011.01.007 | Journal of Symbolic Computation |
Keywords | DocType | Volume |
steiner complex,century theory,gram matrix,gram spectrahedra,semidefinite programming,complex projective plane,cayley octad,plane curves,vinnikov quartic,gale duality,determinantal representations,plane quartic,bitangents,quartic curve,inequivalent representation,sums of squares,exact algorithm,projective plane,algebraic geometry,symbolic computation | Journal | 46 |
Issue | ISSN | Citations |
6 | Journal of Symbolic Computation | 17 |
PageRank | References | Authors |
2.90 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel Plaumann | 1 | 38 | 8.86 |
| Bernd Sturmfels | 2 | 926 | 136.85 |
| Cynthia Vinzant | 3 | 79 | 11.85 |