Symplectic 4-manifolds with arbitrary fundamental group near the Bogomolov--Miyaoka--Yau line

In this paper, we construct a family of symplectic 4-manifolds with positive signature for any given fundamental group G that approaches the BMY line. The family is used to show that one cannot hope to do better than the BMY inequality in finding a lower bound for the function $f=\chi+b\sigma$ on the class of all minimal symplectic 4-manifolds with a given fundamental group.

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Published 1 January 2006