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

摘要

In [8,5], 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) over bar (2) for each integer n >= 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 [8,5]. 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) over bar (2)for each integer n >= 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 c(1)(2) = 9 chi(h) = 45, along with the exotic symplectic 4-manifolds constructed in [2,6,4,7,11]. (C) 2016 Elsevier B.V. All rights reserved.