{"paper":{"title":"On asymptotic behavior of the second Chern forms on degenerating K\\\"ahler-Einstein surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Itsuki Tazoe","submitted_at":"2025-05-03T10:07:05Z","abstract_excerpt":"We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of K\\\"ahler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber integrals of the forms with a smooth test function on the family. We show a lower bound of the H\\\"older exponent of the function at the origin. Our main results consists of two cases: one is a bound of H\\\"older exponent along a line for cscK-metrics, using Biquard-Rollin's a priori estimates for cscK-metrics, and the other is a bound of H\\\"older exponent at the or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01773","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.01773/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}