Simply connected minimal symplectic 4-manifolds with signature less than −1

Abstract

For each pair (e,σ) of integers satisfying 2_e_ + 3_σ_ ≥ 0, σ ≤ −2, and e + σ ≡ 0 (mod 4), with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic e and signature σ. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (resp. signature −1) with Euler characteristic 4_k_ (resp. 4_k_ + 1) for all k ≥ 46 (resp. k ≥ 49).