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• W2950125243 abstract "Let $(L, h)to (X, omega)$ denote a polarized toric Kahler manifold. Fix a toric submanifold $Y$ and denote by $hat{rho}_{tk}:Xto mathbb{R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$, for fixed $t>0$ such that $tkin mathbb{N}$. We prove the existence of a distributional expansion of $hat{rho}_{tk}$ as $kto infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a direct proof that if $omega$ has constant scalar curvature, then $(X, L)$ must be slope semi-stable with respect to $Y$. Similar results are also obtained for more general partial density functions. These results have analogous applications to the study of toric K-stability of toric varieties." @default.
• W2950125243 created "2019-06-27" @default.
• W2950125243 creator A5018027629 @default.
• W2950125243 creator A5071271321 @default.
• W2950125243 date "2011-11-22" @default.
• W2950125243 modified "2023-10-01" @default.
• W2950125243 title "Toric partial density functions and stability of toric varieties" @default.
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• W2950125243 hasPublicationYear "2011" @default.
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