{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:13:31Z","timestamp":1776795211731,"version":"3.51.2"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"278","license":[{"start":{"date-parts":[[2012,9,30]],"date-time":"2012-09-30T00:00:00Z","timestamp":1348963200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We find formulas for the birational maps from a Kummer surface\n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \\mathcal {K}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and its dual\n \n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n \u2217\n \n <\/mml:mo>\n <\/mml:msup>\n \\mathcal {K}^*<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n to their common minimal desingularization\n \n \n \n \n S<\/mml:mi>\n <\/mml:mrow>\n \\mathcal {S}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . We show how the nodes of\n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \\mathcal {K}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and\n \n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n \u2217\n \n <\/mml:mo>\n <\/mml:msup>\n \\mathcal {K}^*<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n blow up. Then we give a description of the group of linear automorphisms of\n \n \n \n \n S<\/mml:mi>\n <\/mml:mrow>\n \\mathcal {S}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/s0025-5718-2011-02547-0","type":"journal-article","created":{"date-parts":[[2011,9,30]],"date-time":"2011-09-30T13:34:10Z","timestamp":1317389650000},"page":"1149-1161","source":"Crossref","is-referenced-by-count":0,"title":["Explicit computations on the desingularized Kummer surface"],"prefix":"10.1090","volume":"81","author":[{"given":"V.","family":"Neumann","sequence":"first","affiliation":[]},{"given":"Constantin","family":"Manoil","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2011,9,30]]},"reference":[{"key":"1","series-title":"Ast\\'{e}risque, No. 54","volume-title":"Surfaces alg\\'{e}briques complexes","author":"Beauville, Arnaud","year":"1978"},{"issue":"269","key":"2","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1090\/S0025-5718-09-02264-9","article-title":"Tate-Shafarevich groups and \ud835\udc3e3 surfaces","volume":"79","author":"Corn, Patrick","year":"2010","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","series-title":"London Mathematical Society Lecture Note Series","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526084","volume-title":"Prolegomena to a middlebrow arithmetic of curves of genus $2$","volume":"230","author":"Cassels, J. W. S.","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/0521483700"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1017\/S0305004100068729","article-title":"The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field","volume":"107","author":"Flynn, Eugene Victor","year":"1990","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"key":"5","series-title":"Pure and Applied Mathematics","isbn-type":"print","volume-title":"Principles of algebraic geometry","author":"Griffiths, Phillip","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0471327921"},{"key":"6","series-title":"Cambridge Mathematical Library","isbn-type":"print","volume-title":"Kummer's quartic surface","author":"Hudson, R. W. H. T.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0521397901"},{"issue":"265","key":"7","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1090\/S0025-5718-08-02105-4","article-title":"Nontrivial elements of Sha explained through \ud835\udc3e3 surfaces","volume":"78","author":"Logan, Adam","year":"2009","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","unstructured":"V.G. Lopez-Neumann and C. Manoil, Explicit computations on the desingularized Kummer surface, arXiv:0906.0790v1."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2012-81-278\/S0025-5718-2011-02547-0\/S0025-5718-2011-02547-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2012-81-278\/S0025-5718-2011-02547-0\/S0025-5718-2011-02547-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:09:53Z","timestamp":1776791393000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2012-81-278\/S0025-5718-2011-02547-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,30]]},"references-count":8,"journal-issue":{"issue":"278","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["S0025-5718-2011-02547-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2011-02547-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2011,9,30]]}}}