{"paper":{"title":"The adapted hyper-K\\\"ahler structure on the crown domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Andrea Iannuzzi, Laura Geatti","submitted_at":"2017-11-05T15:51:54Z","abstract_excerpt":"Let $\\,\\Xi\\,$ be the crown domain associated with a non-compact irreducible hermitian symmetric space $\\,G/K$. We give an explicit description of the unique $\\,G$-invariant adapted hyper-K\\\"ahler structure on $\\,\\Xi$,$\\ $i.$\\,$e.$\\ $compatible with the adapted complex structure $\\,J_{ad}\\,$ and with the $\\,G$-invariant K\\\"ahler structure of $\\,G/K$. We also compute invariant potentials of the involved K\\\"ahler metrics and the associated moment maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01605","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":""},"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"}