On the 7th order ODE with submaximal symmetry

Details On the 7th order ODE with submaximal symmetry On the 7th order ODE with submaximal symmetry

2010-02-08

arxiv.org/abs/1002.1620v3

Mathematics

Differential Geometry

6 pages, 2 figures. Final version - to appear in JGP

Scientific paper

We find a general solution to the unique 7th order ODE admitting ten
dimensional group of contact symmetries. The integral curves of this ODE are
rational contact curves in $\PP^3$ which give rise to rational plane curves of
degree six. The moduli space of these curves is a real form of the homogeneous
space $Sp(4)/SL(2)$.

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