{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T06:50:45Z","timestamp":1772520645388,"version":"3.50.1"},"reference-count":0,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2001,6,14]],"date-time":"2001-06-14T00:00:00Z","timestamp":992476800000},"content-version":"unspecified","delay-in-days":44,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. Lond. Math. Soc."],"published-print":{"date-parts":[[2001,5]]},"abstract":"<jats:p>A minimal surface of general type with <jats:italic>p<\/jats:italic><jats:sub><jats:italic>g<\/jats:italic><\/jats:sub>(<jats:italic>S<\/jats:italic>) = 0 satisfies 1 [les     ] <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup> [les     ] 9, and it is known that the image \nof the bicanonical map \u03c6 is a surface for <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> [ges     ] 2, whilst for <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> [ges     ] 5, the bicanonical map is always a \nmorphism. In this paper it is shown that \u03c6 is birational if <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 9, and that the degree of \u03c6 is at most 2 if <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 7 or <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 8.<\/jats:p><jats:p>By presenting two examples of surfaces <jats:italic>S<\/jats:italic> with <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 7 and 8 and bicanonical map of degree 2, it is \nalso shown that this result is sharp. The example with <jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 8 is, to our knowledge, a new example of a \nsurface of general type with <jats:italic>p<\/jats:italic><jats:sub><jats:italic>g<\/jats:italic><\/jats:sub> = 0.<\/jats:p><jats:p>The degree of \u03c6 is also calculated for two other known surfaces of general type with <jats:italic>p<\/jats:italic><jats:sub><jats:italic>g<\/jats:italic><\/jats:sub> = 0 and \n<jats:italic>K<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>S<\/jats:italic><\/jats:sub> = 8. In both cases, the bicanonical map turns out to be birational.<\/jats:p>","DOI":"10.1017\/s0024609301008037","type":"journal-article","created":{"date-parts":[[2008,2,22]],"date-time":"2008-02-22T08:56:21Z","timestamp":1203670581000},"page":"265-274","source":"Crossref","is-referenced-by-count":20,"title":["THE BICANONICAL MAP OF SURFACES WITH <i>p<\/i><sub><i>g<\/i><\/sub> = 0 AND <i>K<\/i><sup>2<\/sup> [ges     ] 7"],"prefix":"10.1112","volume":"33","author":[{"given":"MARGARIDA MENDES","family":"LOPES","sequence":"first","affiliation":[]},{"given":"RITA","family":"PARDINI","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2001,6,14]]},"container-title":["Bulletin of the London Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1017%2FS0024609301008037","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0024609301008037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T16:43:12Z","timestamp":1554741792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0024609301008037\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,5]]}},"alternative-id":["S0024609301008037"],"URL":"https:\/\/doi.org\/10.1017\/s0024609301008037","relation":{},"ISSN":["0024-6093","1469-2120"],"issn-type":[{"value":"0024-6093","type":"print"},{"value":"1469-2120","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,5]]}}}