  The adiabatic limit procedure associates with every solution of Abelian Higgs
model in (2+1) dimensions a geodesic in the moduli space of static solutions.
We show that the same procedure for Seiberg--Witten equations on 4-dimensional
symplectic manifolds introduced by Taubes may be considered as a complex
(2+2)-dimensional version of the (2+1)-dimensional picture. More precisely, the
adiabatic limit procedure in the 4-dimensional case associates with a solution
of Seiberg--Witten equations a pseudoholomorphic divisor which may be treated
as a complex version of a geodesic in (2+1)-dimensional case.
