{"paper":{"title":"ECH embedding obstructions for rational surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Ben Wormleighton, Julian Chaidez","submitted_at":"2020-08-23T22:52:26Z","abstract_excerpt":"Let $(Y,A)$ be a smooth rational surface or a possibly singular toric surface with ample divisor $A$. We show that a family of ECH-based, algebro-geometric invariants $c^{\\text{alg}}_k(Y,A)$ proposed by Wormleighton obstruct symplectic embeddings into $Y$. Precisely, if $(X,\\omega_X)$ is a $4$-dimensional star-shaped domain and $\\omega_Y$ is a symplectic form Poincar\\'e dual to $[A]$ then \\[(X,\\omega_X)\\text{ embeds into }(Y,\\omega_Y)\\text{ symplectically } \\implies c^{\\text{ECH}}_k(X,\\omega_X) \\le c^{\\text{alg}}_k(Y,A)\\] We give three applications to toric embedding problems: (1) these obstru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.10125","kind":"arxiv","version":3},"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/2008.10125/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"}