For every ruled surface over a positive-genus base surface, the space of symplectic forms in any class of positive self-intersection has infinitely many connected components.
A note on a nontrivial connected component of the space of symplectic structures
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abstract
This note provides the first example of a nontrivial connected component of the space of symplectic structures standard at infinity in dimension four.
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2025 1verdicts
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Infinite connected components of the space of symplectic forms on ruled surfaces
For every ruled surface over a positive-genus base surface, the space of symplectic forms in any class of positive self-intersection has infinitely many connected components.