{"paper":{"title":"Resolution a la Kronheimer of $\\mathbb{C}^3/\\Gamma$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.CV","math.MP"],"primary_cat":"math.DG","authors_text":"Dario Martelli, Massimo Bianchi, Pietro Fr\\'e, Ugo Bruzzo","submitted_at":"2021-05-25T07:07:15Z","abstract_excerpt":"We analyze the relevance of the generalized Kronheimer construction for the gauge-gravity correspondence. We study the general structure of IIB supergravity D3-brane solutions on crepant resolutions $Y$ of singularities $\\mathbb{C}^3/\\Gamma$ with $\\Gamma$ a finite subgroup of $SU(3)$. Next we concentrate on another essential item for the D3-brane construction, i.e., the existence of a Ricci-flat metric on $Y$, with particular attention to the case $\\Gamma=\\mathbb{Z}_4$. We conjecture that on the exceptional divisor the Kronheimer K\\\"ahler metric and the Ricci-flat one, that is locally flat at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11704","kind":"arxiv","version":1},"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/2105.11704/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"}