| Autor: |
Biliotti, Leonardo, Windare, Oluwagbenga Joshua |
| Předmět: |
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| Zdroj: |
Journal of Geometric Analysis; Mar2023, Vol. 33 Issue 3, p1-31, 31p |
| Abstrakt: |
We presented a systematic treatment of a Hilbert criterion for stability theory for an action of a real reductive group G on a real submanifold X of a Kähler manifold Z. More precisely, we suppose that the action of a compact Lie group U with Lie algebra u extends holomorphically to an action of the complexified group U C and that the U-action on Z is Hamiltonian. If G ⊂ U C is compatible, there is a corresponding gradient map μ p : X → p , where g = k ⊕ p is a Cartan decomposition of the Lie algebra of G. The concept of energy complete action of G on X is introduced. For such actions, one can characterize stability, semistability and polystability of a point by a numerical criteria using a G-equivariant function called maximal weight. We also prove the classical Hilbert–Mumford criteria for semistability and polystability conditions. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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