On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature

In [8] and [5], the first author and his collaborators constructed the irreducible symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n−1)CP2#(2n−1)CP‾2 for each integer n≥25n≥25, and the families of simply connected irreducible nonspin symplectic 4-manifolds with positive signature that are interesting with respect to the symplectic geography problem. In this paper, we improve the main results in [8] and [5]. In particular, we construct (i) an infinitely many irreducible symplectic and nonsymplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n−1)CP2#(2n−1)CP‾2 for each integer n≥12n≥12, and (ii) the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signature and with more than one smooth structure. Our construction uses the complex surfaces of Hirzebruch and Bauer–Catanese on Bogomolov–Miyaoka–Yau line with c12=9χh=45, along with the exotic symplectic 4-manifolds constructed in [2], [6], [4], [7] and [11].