{"paper":{"title":"Toric partial density functions and stability of toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.SG"],"primary_cat":"math.DG","authors_text":"Florian T. Pokorny, Michael Singer","submitted_at":"2011-11-22T17:32:19Z","abstract_excerpt":"Let $(L, h)\\to (X, \\omega)$ denote a polarized toric K\\\"ahler manifold. Fix a toric submanifold $Y$ and denote by $\\hat{\\rho}_{tk}:X\\to \\mathbb{R}$ 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 $tk\\in \\mathbb{N}$. We prove the existence of a distributional expansion of $\\hat{\\rho}_{tk}$ as $k\\to \\infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5259","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}