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A note on the geography of symplectic manifolds. (English) Zbl 0876.57039
Theorem: If \((a,b)\in{\mathbb Z}^2\), \(0<b<2a-6\) and \(b\) is even, then there exists a minimal symplectic manifold \(X\) such that \((\chi(X),c_1^2(X))=(a,b)\) where \(\chi(X)\) is the holomorphic Euler characteristic and \(c_1(X)\) is the first Chern class. The proof uses Donaldson series [S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds (1990; Zbl 0820.57002)].

MSC:
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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