{"paper":{"title":"Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Han Zhang, Yifan Chen, YongJoo Shin","submitted_at":"2025-07-02T06:48:46Z","abstract_excerpt":"Lee and the second named author studied involutions on smooth minimal surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. They gave the possibilities of the birational models $W$ of the quotients and the branch divisors $B_0$ induced by involutions $\\sigma$ on the surfaces $S$.\n  In this paper we improve and refine the results of Lee and the second named author. We exclude the case of the Kodaira dimension $\\kappa(W)=1$ when the number $k$ of isolated fixed points of an involution $\\sigma$ on $S$ is nine. The possibilities of branch divisors $B_0$ are reduced for the case $k=9$, and ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01405","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/2507.01405/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"}