Small exotic 4-manifolds from lines and quadrics in CP2.

We construct potentially new manifolds homeomorphic but not diffeomorphic to CP 2 # 8 CP 2 ¯ and CP 2 # 9 CP 2 ¯ via rational blowdown surgery along certain 4-valent plumbing graphs. This way all the graph classes from [5] have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize the simplicity of the constructions which boils down to finding a good configuration of complex lines and quadrics in CP 2 , and deciding which intersections to blow up. [ABSTRACT FROM AUTHOR]