  In higher dimensional gauge theory, we need energies with higher power terms
of field strength in order to realize point-wise monopoles. We consider new
models with higher power terms of field strength and extraordinary kinetic term
of scalar field. Monopole charges are computed as integrals over spheres and
they are related to mapping class degree. Hedge-Hog solutions are investigated
in these models. Every differential equation for these solutions is Abel's
differential equation. A condition for existence of finite energy solution is
shown. Spaces of 1-jets of these equations are defined as sets of zeros of
polynomials. Those spaces can be interpreted as singular quartic surfaces in
three-dimensional complex projective space.
