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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.)
##### Keywords:
symplectic manifolds; characteristic classes