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A remark about Donaldson’s construction of symplectic submanifolds. (English) Zbl 1171.53343

Summary: We describe a simplification of S. K. Donaldson’s arguments for the construction of symplectic hypersurfaces [J. Differ. Geom. 44, No. 4, 666–705 (1996; Zbl 0883.53032)] or Lefschetz pencils [J. Differ. Geom. 53, No. 2, 205–236 (1999; Zbl 1040.53094)] that makes it possible to avoid any reference to Yomdin’s work on the complexity of real algebraic sets.

MSC:

53D35 Global theory of symplectic and contact manifolds
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