Kähler-Einstein metrics on group compactifications
| Autor: | Thibaut Delcroix |
|---|---|
| Přispěvatelé: | École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics group compactification Polytope Fano plane 01 natural sciences Mathematics - Algebraic Geometry symbols.namesake Monge-Ampère Greatest ricci lower bound 0103 physical sciences 0101 mathematics Einstein Mathematics::Symplectic Geometry Mathematics 010102 general mathematics Reductive group Invariant (physics) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] polytope symbols 010307 mathematical physics Geometry and Topology [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Kähler-Einstein Analysis Maximal compact subgroup |
| Zdroj: | Geometric And Functional Analysis Geometric And Functional Analysis, 2017, 27 (1), pp.78-129. ⟨10.1007/s00039-017-0394-y⟩ |
| DOI: | 10.1007/s00039-017-0394-y⟩ |
| Popis: | International audience; We obtain a necessary and sufficient condition of existence of a Kähler-Einstein metric on a $G\times G$-equivariant Fano compactification of a complex connected reductive group $G$ in terms of the associated polytope. This condition is not equivalent to the vanishing of the Futaki invariant. The proof relies on the continuity method and its translation into a real Monge-Ampère equation, using the invariance under the action of a maximal compact subgroup $K\times K$. |
| Databáze: | OpenAIRE |
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