Moduli of Curves

1. Front Matter

   Pages i-ix

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2. Lectures on Tropical Curves and Their Moduli Spaces

   • Melody Chan

   Pages 1-26

3. Higher Dimensional Varieties and their Moduli Spaces

   • Paolo Cascini

   Pages 27-47

4. Higher-Dimensional Varieties

   • Olivier Debarre

   Pages 49-106

5. Progress on Syzygies of Algebraic Curves

   • Gavril Farkas

   Pages 107-138

6. Lectures on Bridgeland Stability

   • Emanuele Macrì, Benjamin Schmidt

   Pages 139-211

7. Algebraic Curves and Their Moduli

   • E. Sernesi

   Pages 213-239

8. Back Matter

   Pages 241-242

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Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. The book collects the lecture notes of a number of leading algebraic geometers and in particular specialists in the field of moduli spaces of curves and their geometry. This is an important subject in algebraic geometry and complex analysis which has seen spectacular developments in recent decades, with important applications to other parts of mathematics such as birational geometry and enumerative geometry, and to other sciences, including physics. The themes treated are classical but with a constant look to modern developments (see Cascini, Debarre, Farkas, and Sernesi's contributions), and include very new material, such as Bridgeland stability (see Macri's lecture notes) and tropical geometry (see Chan's lecture notes).

• 14D20,14D22,14H10,14E30,14N05,14F05,14T05
• Curves
• Moduli spaces
• Birational Geometry
• Projective Geometry
• Varieties
• Tropical geometry
• Sygygies
• Vector Bundles
• Bridgeland Stability

• CIMAT, Guanajuato, Mexico

  Leticia Brambila Paz

• Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy

  Ciro Ciliberto

• Instituto Nacional de Matemática Pura, Rio de Janeiro, Brazil

  Eduardo Esteves

• Dipartimento di Matematica, Università di Roma Tre, Roma, Italy

  Margarida Melo

• Collège de France, Paris, France

  Claire Voisin

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