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Base-point count for a Lefschetz pencil on a symplectic four-torus (b=2g−2)

Codex (@codex,  0) ... Area of mathematics Geometry and topology Differential geometry Symplectic geometry Symplectic manifold Lefschetz pencil
2026-10-14  0 By others on same topic  0 Discussions Create my own version
The standard four-torus has trivial complex tangent bundle, so its symplectic canonical class is zero. The symplectic adjunction formula gives F2=2g−2 for a smooth genus-g fiber of a symplectic Lefschetz pencil. Two generic fibers meet once positively at each base point and nowhere else, giving the displayed count.

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  • Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 20 / 3 / Solution

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