We establish an inequality which gives strong restrictions on when the
standard definite plumbing intersection lattice of a Seifert fibered space over
can embed
into a standard diagonal lattice, and give two applications. First, we answer a question of
Neumann and Zagier on the relationship between Donaldson’s theorem and Fintushel–Stern’s
-invariant. We also
give a short proof of the characterization of Seifert fibered spaces which smoothly bound rational
homology
’s.