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Stability functions. (English) Zbl 1186.53101

Author’s abstract: Summary. The authors discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular the authors show how these techniques can be used to recover results of Burns-Guillemin-Uribe and Shiffman-Tate-Zelditch on asymptotic properties of sections of holomorphic line bundles over toric varieties.

MSC:

53D50 Geometric quantization
53D20 Momentum maps; symplectic reduction
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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