Compact moduli spaces of surfaces of general type

Details Compact moduli spaces of surfaces of general type Compact moduli spaces of surfaces of general type

2011-07-14

arxiv.org/abs/1107.2717v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divisor by Alexeev. The construction is an application of Mori's minimal model program for 3-folds. We review the example of the projective plane with a curve of degree d > 3. We explain a connection between the geometry of the boundary of the compactification of the moduli space and the classification of vector bundles on the surface in the case H^{2,0}=H^1=0.

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