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In this paper we prove that the Torelli part of the symplectomorphism groupsof the $n$-point ($n\leq 4$) blow-ups of the projective plane is trivial.Consequently, we determine the symplectic mapping class group. It is generatedby reflections on $K_{\omega}- $spherical class with zero $\omega$ area.

The symplectic mapping class group of $\CC P^2 n{\bar{\CC P^2}}$ with $n\leq4$