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A Superficial Working Guide to Deformations and Moduli
This is the first part of a guide to deformations and moduli, especially
viewed from the perspective of algebraic surfaces (the simplest higher
dimensional varieties). It contains also new results, regarding the question of
local homeomorphism between Kuranishi and Teichmueller space, and a survey of
new results with Ingrid Bauer, concerning the discrepancy between the
deformation of the action of a group G on a minimal models S, respectively the
deformation of the action of G on the canonical model X. Here Def(S) maps
properly onto Def(X), but the same does not hold for pairs: Def(S,G) does not
map properly onto Def(X,G). Indeed the connected components of Def(S), in the
case of tertiary Burniat surfaces, only map to locally closed sets. The last
section contains anew result on some surfaces whise Albanese map has generic
degree equal to 2.Comment: 56 pages, revision to appear in the Handbook of Moduli, in honour of
David Mumford, to be published by International press, editors Gavril Farkas
and Ian Morrison. The former theorem 29 on moduli spaces for minimal surfaces
has been correcte
Notes on a paper of Mess
These notes are a companion to the article "Lorentz spacetimes of constant
curvature" by Geoffrey Mess, which was first written in 1990 but never
published. Mess' paper will appear together with these notes in a forthcoming
issue of Geometriae Dedicata.Comment: 26 page
The structure of algebraic varieties
ICM lecture on minimal models and moduli of varieties
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