Singular Kähler-Einstein metrics on $ \mathbb Q $-Fano compactifications of Lie groups
Description
In this paper, we prove an existence result for Kähler-Einstein metrics on $ \mathbb Q $-Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a fine condition. As an application, we prove that there is no $ \mathbb Q $-Fano $ {\rm SO}_4(\mathbb C) $-compactification which admits a Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano $ {\rm SO}_4(\mathbb C) $-compactification.
Translated Descriptions
Translated Description (Arabic)
في هذه الورقة، نثبت وجود نتيجة لمقاييس Kähler - Einstein على $\mathbb Q $ - Fano compactifications لمجموعات LIE بالطريقة المتغيرة، بشرط أن تفي متعددات العزم بحالة دقيقة</ italic>. كتطبيق، نثبت أنه لا يوجد ضغط $\mathbb Q $- Fano ${\ rm SO }_ 4(\mathbb C )$ الذي يقبل مقياس كالر- آينشتاين بنفس حجم ضغط K - unstable Fano ${\ rm SO }_4 (\mathbb C )$.</ abstract>
Translated Description (French)
Dans cet article, nous prouvons un résultat d'existence pour les métriques de Kähler-Einstein sur les compactifications $ \mathbb Q $ -Fano des groupes de Lie par la méthode variationnelle, à condition que leurs polytopes de moment satisfassent une condition fine. En tant qu'application, nous prouvons qu'il n'y a pas de $ \mathbb Q $ -Fano $ {\rm SO}_4(\mathbb C) $ -compactification qui admette une métrique de Kähler-Einstein avec le même volume que celui d'une Fano K-instable lisse $ {\rm SO}_4(\mathbb C) $ -compactification.
Translated Description (Spanish)
En este artículo, demostramos un resultado de existencia para las métricas de Kähler-Einstein en $ \mathbb Q $-Fano compactaciones de grupos de Lie por el método variacional, siempre que sus politopos de momento satisfagan una condición fina. Como aplicación, demostramos que no hay una $ \mathbb Q $-Fano $ {\rm SO}_4(\mathbb C) $ -compactificación que admita una métrica de Kähler-Einstein con el mismo volumen que la de un Fano K-inestable suave $ {\rm SO}_4(\mathbb C) $ -compactificación.
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2001.11320.pdf
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Additional details
Additional titles
- Translated title (Arabic)
- مقاييس كالر- آينشتاين الفردية على $\mathbb Q $ -ضغط فانو لمجموعات LIE
- Translated title (French)
- Métriques singulières de Kähler-Einstein sur $ \mathbb Q $-Fano compactifications des groupes de Lie
- Translated title (Spanish)
- Métricas singulares de Kähler-Einstein en $ \mathbb Q $-Fano compactaciones de grupos de Lie
Identifiers
- Other
- https://openalex.org/W3003443099
- DOI
- 10.3934/mine.2023028
References
- https://openalex.org/W1498456576
- https://openalex.org/W1504483056
- https://openalex.org/W1582015855
- https://openalex.org/W1793192312
- https://openalex.org/W1973792696
- https://openalex.org/W1994934481
- https://openalex.org/W2015717514
- https://openalex.org/W2018408650
- https://openalex.org/W2024144957
- https://openalex.org/W2027029357
- https://openalex.org/W2028712970
- https://openalex.org/W2041872613
- https://openalex.org/W2063281701
- https://openalex.org/W2076559073
- https://openalex.org/W2077339801
- https://openalex.org/W2088508493
- https://openalex.org/W2091208721
- https://openalex.org/W2132525987
- https://openalex.org/W2202286330
- https://openalex.org/W2315478648
- https://openalex.org/W2503794145
- https://openalex.org/W2570500637
- https://openalex.org/W2962730227
- https://openalex.org/W2962745321
- https://openalex.org/W2962815572
- https://openalex.org/W2963011588
- https://openalex.org/W2963435898
- https://openalex.org/W2963506819
- https://openalex.org/W2963552219
- https://openalex.org/W2963754085
- https://openalex.org/W2990482950
- https://openalex.org/W3013167422
- https://openalex.org/W3056521201
- https://openalex.org/W3081552865
- https://openalex.org/W3083682397
- https://openalex.org/W3088030151
- https://openalex.org/W3099153359
- https://openalex.org/W3122157122
- https://openalex.org/W3192203038
- https://openalex.org/W3206875499
- https://openalex.org/W4246077597