{"paper":{"title":"Sharp systolic inequalities for K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MG"],"primary_cat":"math.DG","authors_text":"Raphael Tsiamis","submitted_at":"2026-05-19T17:59:08Z","abstract_excerpt":"We establish sharp inequalities for two-dimensional systolic invariants of metrics with positive scalar curvature: the $2$-systole and the spherical $2$-systole of compact K\\\"ahler manifolds, and the stable $2$-systole of Riemannian metrics on a general class of $\\mathrm{spin}^c$ manifolds and their products. These bounds attain equality precisely for complex projective space $\\mathbb{CP}^n$ equipped with the Fubini--Study metric, and admit further refinements for Fano manifolds which distinguish the complex quadric, cubic, and quartic with their canonical K\\\"ahler--Einstein structures. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20178","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/2605.20178/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"}