Algebraic and Complex Geometry

1. Front Matter

   Pages i-xii

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2. Stability Conditions and Positivity of Invariants of Fibrations

   • M. A. Barja, L. Stoppino

   Pages 1-40

3. On the Second Lower Quotient of the Fundamental Group

   • Arnaud Beauville

   Pages 41-45

4. McKay Correspondence over Non Algebraically Closed Fields

   • Mark Blume

   Pages 47-75

5. Gonality of Algebraic Curves and Graphs

   • Lucia Caporaso

   Pages 77-108

6. Caustics of Plane Curves, Their Birationality and Matrix Projections

   • Fabrizio Catanese

   Pages 109-121

7. Limits of Pluri–Tangent Planes to Quartic Surfaces

   • Ciro Ciliberto, Thomas Dedieu

   Pages 123-199

8. On Images of Weak Fano Manifolds II

   • Osamu Fujino, Yoshinori Gongyo

   Pages 201-207

9. The Hyperholomorphic Line Bundle

   • Nigel Hitchin

   Pages 209-223

10. Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems

    • Henning Hollborn, Stefan Müller–Stach

    Pages 225-240

11. Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3^[n]-Type

    • Eyal Markman

    Pages 241-283

12. Contact Kähler Manifolds: Symmetries and Deformations

    • Thomas Peternell, Florian Schrack

    Pages 285-308

13. Back Matter

    Pages 309-319

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Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the first author. It also includes a full list of speakers with all titles and abstracts.

• 14J10, 14E30, 14J28, 14J32, 14J50, 14T05
• geometry of moduli spaces
• hyperkähler manifolds
• irreducible symplectic manifolds

• Leibniz Universität Hannover, Hannover, Germany

  Anne Frühbis-Krüger, Matthias Schütt

• Humboldt-University Berlin, Berlin, Germany

  Remke Nanne Kloosterman

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