Lefschetz pencils, branched covers and symplectic invariants

Details Lefschetz pencils, branched covers and symplectic invariants Lefschetz pencils, branched covers and symplectic invariants

2004-01-04

arxiv.org/abs/math/0401021v1

Mathematics

Symplectic Geometry

44 pages; lectures given at the CIME summer school "Symplectic 4-manifolds and algebraic surfaces", Cetraro (Italy), September

Scientific paper

This set of lectures aims to give an overview of Donaldson's theory of linear systems on symplectic manifolds and the algebraic and geometric invariants to which they give rise. After collecting some of the relevant background, we discuss topological, algebraic and symplectic viewpoints on Lefschetz pencils and branched covers of the projective plane. The later lectures discuss invariants obtained by combining this theory with pseudo-holomorphic curve methods.

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