Slope inequalities for the geography problem of nonspin symplectic 4-manifolds

Abstract

Given an ordered pair of positive integers (e,σ), we can ask whether the pair is realizable as the Euler characteristic and the signature of a closed simply connected nonspin minimal symplectic 4-manifold. It is well known that for any fixed signature value σ>0, the pair is realizable if the Euler characteristic value e is large enough relative to σ. In this paper, we discuss just how large e might have to be asymptotically as we let σ→∞.