{"paper":{"title":"Moduli spaces of quadratic rational maps with a marked periodic point of small order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"J. Blanc, J.K. Canci, N. D. Elkies","submitted_at":"2013-05-05T21:29:51Z","abstract_excerpt":"The surface corresponding to the moduli space of quadratic endomorphisms of $\\mathbb{P}^1$ with a marked periodic point of order $n$ is studied. It is shown that the surface is rational over $\\mathbb{Q}$ when $n\\le 5$ and is of general type for $n=6$.\n  An explicit description of the $n=6$ surface lets us find several infinite families of quadratic endomorphisms $f: \\mathbb{P}^1 \\to \\mathbb{P}^1$ defined over $\\mathbb{Q}$ with a rational periodic point of order $6$. In one of these families, $f$ also has a rational fixed point, for a total of at least $7$ periodic and $7$ preperiodic points. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1054","kind":"arxiv","version":2},"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"}