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Lefschetz Pencils, Branched Covers and Symplectic Invariants

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Symplectic 4-Manifolds and Algebraic Surfaces

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1938))

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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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA

    Denis Auroux

  2. Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WB, Cambridge, UK

    Ivan Smith

Authors
  1. Denis Auroux
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  2. Ivan Smith
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Editor information

Editors and Affiliations

  1. Mathematisches Institut Lehrstuhl Mathematik VIII, Universität Bayreuth, 95447, Bayreuth, Germany

    Fabrizio Catanese

  2. Department of Mathematics, Princeton University, Washington Road, 08544-1000, Princeton, NJ, USA

    Gang Tian

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Auroux, D., Smith, I. (2008). Lefschetz Pencils, Branched Covers and Symplectic Invariants. In: Catanese, F., Tian, G. (eds) Symplectic 4-Manifolds and Algebraic Surfaces. Lecture Notes in Mathematics, vol 1938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78279-7_1

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