{"paper":{"title":"A generalised cross-ratio and limits of local heights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Emre Can Sert\\\"oz, Hidde Lammert Bakker","submitted_at":"2026-07-07T16:33:33Z","abstract_excerpt":"We generalise the standard cross-ratio of four points on a projective line to a cross-ratio of a configuration of four planes in projective $n$-space, the first pair $A_1,\\,A_2$ being $k$-dimensional and the second pair $B_1,\\,B_2$ being $(n-k-1)$-dimensional, with $A_i \\cap B_j = \\emptyset$. Over the complex numbers, we show that this cross-ratio equals the augmented height pairing of the corresponding cycles $A_1-A_2, \\, B_1-B_2$. Over a discretely valued field, we show that the valuation of the cross-ratio equals the intersection degree of the cycles once they are spread out over the valuat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06477","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/2607.06477/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"}