Handbook of Moduli: Volumes I, II, III (3-volume set)

The Handbook of Moduli, comprising three volumes, offers a multi-faceted survey of a rapidly developing subject aimed not just at specialists but at a broad community of producers of algebraic geometry, and even at some consumers from cognate areas. The thirty-five articles in the Handbook, written by fifty leading experts, cover nearly the entire range of the field. They reveal the relations between these many threads and explore their connections to other areas of algebraic geometry, number theory, differential geometry, and topology. The goals of the Handbook are to introduce the techniques, examples, and results essential to each topic, and to say enough about recent developments to provide a gateway to the primary sources. Many articles are original treatments commissioned to bridge gaps in the literature and to make important problems accessible to a wide audience for the first time, and many others illustrate yogas and heuristics that experts use privately to guide intuition or simplify calculation, but that do not appear in published work aimed at other specialists.

Gavril Farkas is Professor of Mathematics at the Humboldt Universitaet zu Berlin. He has also taught at the University of Texas, the University of Michigan, and Princeton University, and held visiting positions at Harvard University and M.S.R.I. Berkeley. His interests include moduli spaces in algebraic geometry, especially for curves and abelian varieties, and their relations to vector bundles and syzygies.

Ian Morrison is Professor of Mathematics at Fordham University. He has also taught at Columbia University, the University of Toronto, and the University of California at Los Angeles, and has held visiting positions at the University of Sydney, the T.I.F.R. Mumbai, the S.N.S. Pisa, the C.R.M. Barcelona, M.S.R.I. Berkeley, Harvard University, the Universite de Paris-Sud and the Universita di Roma Sapienza. His interests include moduli spaces of curves, geometric invariant theory, and birational geometry, and particularly the interactions between these areas.