Note on new symplectic 4-manifolds with nonnegative signature

2012/07/09 by Anar Akhmedov, Akhmedov, Anar
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1207.1973

openalex publication_date 2012/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we present a construction of new symplectic 4-manifolds with non-negative signature using the complex surfaces on Bogomolov-Miyaoka-Yau line c₁² = 9χ_h, the fake projective planes and Cartwright-Steger surfaces. Our construction yields an infinite family of fake rational homology (2n-1)\CP#(2n-1)\CPb for any integer 3 ≤ n ≤ 22.

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