{"paper":{"title":"Examples of Type IV unprojection","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Miles Reid","submitted_at":"2001-08-06T14:05:26Z","abstract_excerpt":"I show that the weighted projective line PP(2,3) has an embedding PP(2,3) into PP(4,5,6,9) whose image Gamma is contained in a quasismooth K3 hypersurface X_24 in PP(4,5,6,9). The pair (Gamma in X_24) unprojects to the codimension 4 K3 surface Y in PP(4,5,5,6,7,8,9) with\n Basket = [1/2(1,1), 1/5(1,4), 1/5(2,3), 1/9(4,5)],\n Hilbert Numerator = 1 - t^12 - t^13 - 2t^14 - 2t^15 - 2t^16 - t^17\n  + t^19 + 2t^20 + 3t^21 + 4t^2 + 3t^23 + ..\n (this example is called Altinok4(111) in the Magma K3 database). The local coordinates at the third centre P_3 = 1/5(2,3) of Y are of weight 7 and 8 (rather than "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0108037","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"}