[{"_id":"23149","citation":{"mla":"Bernert, Christian, et al. “Integral Points over Number Fields: A Clemens Complex Jigsaw Puzzle.” <i>Mathematische Zeitschrift</i>, vol. 314, no. 3, 37, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s00209-026-04140-2\">10.1007/s00209-026-04140-2</a>.","ama":"Bernert C, Derenthal U, Ortmann J, Wilsch FA. Integral points over number fields: a Clemens complex jigsaw puzzle. <i>Mathematische Zeitschrift</i>. 2026;314(3). doi:<a href=\"https://doi.org/10.1007/s00209-026-04140-2\">10.1007/s00209-026-04140-2</a>","apa":"Bernert, C., Derenthal, U., Ortmann, J., &#38; Wilsch, F. A. (2026). Integral points over number fields: a Clemens complex jigsaw puzzle. <i>Mathematische Zeitschrift</i>. Springer. <a href=\"https://doi.org/10.1007/s00209-026-04140-2\">https://doi.org/10.1007/s00209-026-04140-2</a>","ista":"Bernert C, Derenthal U, Ortmann J, Wilsch FA. 2026. Integral points over number fields: a Clemens complex jigsaw puzzle. Mathematische Zeitschrift. 314(3), 37.","short":"C. Bernert, U. Derenthal, J. Ortmann, F.A. Wilsch, Mathematische Zeitschrift 314 (2026).","ieee":"C. Bernert, U. Derenthal, J. Ortmann, and F. A. Wilsch, “Integral points over number fields: a Clemens complex jigsaw puzzle,” <i>Mathematische Zeitschrift</i>, vol. 314, no. 3. Springer, 2026.","chicago":"Bernert, Christian, Ulrich Derenthal, Judith Ortmann, and Florian Alexander Wilsch. “Integral Points over Number Fields: A Clemens Complex Jigsaw Puzzle.” <i>Mathematische Zeitschrift</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s00209-026-04140-2\">https://doi.org/10.1007/s00209-026-04140-2</a>."},"quality_controlled":"1","status":"public","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"scopus_import":"1","article_type":"original","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Mathematische Zeitschrift","article_number":"37","has_accepted_license":"1","dataavailabilitystatement":"Our manuscript has no associated data.","file_date_updated":"2026-10-19T06:11:23Z","researchdata_availability":"no","das_tickbox":"1","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","oa":1,"year":"2026","date_published":"2026-11-01T00:00:00Z","language":[{"iso":"eng"}],"file":[{"file_size":593086,"file_id":"23160","checksum":"c2157633b4832a760336cd5d3f77b022","creator":"dernst","file_name":"2026_MathemZeitschrift_Bernert.pdf","relation":"main_file","access_level":"open_access","date_created":"2026-10-19T06:11:23Z","success":1,"content_type":"application/pdf","date_updated":"2026-10-19T06:11:23Z"}],"abstract":[{"text":"We prove an asymptotic formula for the number of integral points of bounded log anticanonical height on a singular quartic del Pezzo surface over arbitrary number fields, with respect to the largest admissible boundary divisor. The resulting Clemens complex is more complicated than usual, and leads to particularly interesting effective cone constants, associated with exponentially many polytopes whose volumes appear in the expected formula. Like a jigsaw puzzle, these polytopes fit together to one large polytope. The volume of this polytope appears in the asymptotic formula that we obtain using the universal torsor method via o-minimal structures.","lang":"eng"}],"volume":314,"fulldoi":"https://doi.org/10.1007/s00209-026-04140-2","type":"journal_article","PlanS_conform":"1","month":"11","title":"Integral points over number fields: a Clemens complex jigsaw puzzle","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"ddc":["510"],"arxiv":1,"supplementarymaterial":"no","external_id":{"arxiv":["2601.08774"]},"issue":"3","publication_status":"published","OA_place":"publisher","doi":"10.1007/s00209-026-04140-2","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. We would like to thank the referee for their careful reading and helpful remarks that helped to improve this article. The first two authors were supported by the Deutsche Forschungsgemeinschaft (DFG) – 512730679 (RTG2965). The third author was partially supported by the Caroline Herschel Programme of Leibniz University Hannover. The fourth author was supported by the Deutsche Forschungsgemeinschaft (DFG) – 398436923 (RTG2491).","publisher":"Springer","author":[{"last_name":"Bernert","first_name":"Christian","id":"aefba9fc-4694-11f0-b73e-8bd408e8f734","full_name":"Bernert, Christian"},{"full_name":"Derenthal, Ulrich","first_name":"Ulrich","last_name":"Derenthal"},{"last_name":"Ortmann","full_name":"Ortmann, Judith","first_name":"Judith"},{"last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256","first_name":"Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"date_created":"2026-10-18T22:01:50Z","OA_type":"hybrid","date_updated":"2026-10-19T06:13:10Z","department":[{"_id":"TiBr"}],"intvolume":"       314"}]