A survey of the geometric criterion for Gieseker-Mumford stability of polarized manifolds
Date Issued
2011
Date
2011
Author(s)
Tuan, Shou-Cheng
Abstract
This paper is to study Luo’s paper in 1997. We give four statements with their proofs.
Firstly, Luo introduce the polarized manifold and its Hilbert point. By the stability of Hilbert points in the Geometric Invariant Theory, he defined the stability of polarized manifolds in the Geometric Invariant Theory; hence he gave the proposition for the stability. We prove our first statement.
Secondly, Luo use the differential geometric method to reduce the proposition. By the definition of Green current, it gave the extended proposition for the Gieseker-Mumford stability, which is the first main theorem . Here we prove two statements.
Finally, use the above analysis, Luo proved the last theorem. We prove our final statement and do a slight improvement to give the geometric criterion for the Gieseker-Mumford stability.
Subjects
stability
Hilbert point
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