Every symplectic four-dimensional small cover is aspherical; symplecticity on polygon-product bases equals factor-compatibility, with a non-product example constructed.
Masuda,Cohomological non-rigidity of generalized real Bott manifolds of height 2, Tr
2 Pith papers cite this work. Polarity classification is still indexing.
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Every factor-compatible small cover over a product of polygons admits a smooth projective model as a finite quotient of a product of curves, and the graded mod 2 cohomology ring determines the Hodge diamond of that model.
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Symplectic small covers in dimension four
Every symplectic four-dimensional small cover is aspherical; symplecticity on polygon-product bases equals factor-compatibility, with a non-product example constructed.
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Symplectic and projective small covers over products of polygons
Every factor-compatible small cover over a product of polygons admits a smooth projective model as a finite quotient of a product of curves, and the graded mod 2 cohomology ring determines the Hodge diamond of that model.