Info

This web page is a clone of a web page created by Jeff Giansiracusa and Davesh Maulik. The original version can be accessed at aimath.org/WWN/modspacecurves/glossary/index.html.

This glossary contains brief definitions and explanations of many technical terms that arise is the study of the moduli space of curves. It was produced as part of the activities during the Topology and Geometry of the Moduli space of Curves workshop in March 2005; it is a component of a larger resource site at http://www.aimath.org/WWN/modspacecurves/

Please send comments, suggestions, corrections, etc. to either

• Harry Richman (hrichman@alum.mit.edu)
• or Jeff Giansiracusa (giansira@maths.ox.ac.uk)
• or Davesh Maulik (dmaulik@math.princeton.edu).

• Ample cone
• Arithmetic genus
• Boundary divisors
• Classifying space
• Coarse and fine moduli spaces
• Deligne-Mumford compactification
• Deligne-Mumford stack
• Dyer-Lashof-Araki-Kudo operations
• Effective cone
• Frobenius algebra
• Frobenius manifold
• General type
• Geometric genus
• Gromov-Witten invariants
• Group completion
• Harer stability
• Hodge bundle
• Hodge classes
• Homology fibration
• Hurwitz numbers
• Hurwitz schemes
• Infinite loop space
• Kappa classes
• Kodaira dimension
• Mapping class group
• Moduli space of admissible covers
• Nerve of a category
• Partial compactifications
• Plus construction
• Pontrjagin-Thom construction
• Quantum cohomology
• Slope conjecture
• Spectrum
• String equation
• String topology operations
• Tautological rings
• Teichmuller space
• Torelli group
• Unirational
• Virasoro conjecture
• Virtual fundamental class
• Weil-Petersson metric
• Witten classes
• Witten’s Conjecture