2015/05/31 by Anar Akhmedov, Akhmedov, Anar, Sümeyra Sakallı +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1506.00230
openalex publication_date 2015/05/31 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In citeAP3, AHP, the first author and his collaborators constructed the\nirreducible symplectic 4-manifolds that are homeomorphic but not\ndiffeomorphic to (2n-1) mathbbCP2 #(2n-1)\ mathbbCP2\nfor each integer n \≥ 25, and the families of simply connected irreducible\nnonspin symplectic 4-manifolds with positive signature that are interesting\nwith respect to the symplectic geography problem. In this paper, we improve the\nmain results in citeAP3, AHP. In particular, we construct (i) an infinitely\nmany irreducible symplectic and non-symplectic 4-manifolds that are\nhomeomorphic but not diffeomorphic to\n(2n-1) mathbbCP2 #(2n-1)\ mathbbCP2 for each integer n\n\≥ 12, and (ii) the families of simply connected irreducible nonspin\nsymplectic 4-manifolds that have the smallest Euler characteristics among the\nall known simply connected 4-manifolds with positive signature and with more\nthan one smooth structure. Our construction uses the complex surfaces of\nHirzebruch and Bauer-Catanese on Bogomolov-Miyaoka-Yau line with c12 =\n9\χh = 45, along with the exotic symplectic 4-manifolds constructed in\n citeA4, AP1, ABBKP, AP2, AS.\n