{"paper":{"title":"Embedding more than 8 symplectic balls in $\\mathbb{C}\\mathrm{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Jarek K\\k{e}dra, Martin Pinsonnault, S\\'ilvia Anjos","submitted_at":"2026-05-22T19:32:21Z","abstract_excerpt":"We prove that the space of symplectic embeddings of $n\\geq 1$ standard balls into the standard complex projective plane $\\mathbb{C}\\mathrm{P}^2$ is homotopy equivalent to the configuration space of $n$ points in $\\mathbb{C}\\mathrm{P}^2$, provided that the sum of the capacities of the balls is strictly less than the symplectic area of a line. Moreover, our techniques suggest that, for $n=9$, there are infinitely many homotopy types of spaces of symplectic ball embeddings, depending on the capacities of the balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24161","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/2605.24161/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"}