The GIT-stability of Polarised Varieties via discrepancy

Details The GIT-stability of Polarised Varieties via discrepancy The GIT-stability of Polarised Varieties via discrepancy

2008-07-10

arxiv.org/abs/0807.1716v4

Mathematics

Algebraic Geometry

33 pages, no figure. This paper had been once withdrawn (v3), since the results were too weak for persuasiveness at that momen

Scientific paper

We prove that (various) GIT semistability of polarized varieties implies
semi-log-canonicity, up to the existence of relative log canonical model or its
nonnormal analogue. This generalizes the classical results obtained by Mumford
and Shah for curves and surfaces in 1970s, in terms of discrepancy.

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