{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T07:22:15Z","timestamp":1767856935461,"version":"3.49.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T00:00:00Z","timestamp":1716076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T00:00:00Z","timestamp":1716076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"yFCT\/Portugal through Centro de An\u00e1lise Matem\u00e1tica, Geometria e Sistemas Din\u00e1micos (CAMGSD), IST-ID","award":["UIDB\/04459\/2020 and UIDP\/04459\/2020."],"award-info":[{"award-number":["UIDB\/04459\/2020 and UIDP\/04459\/2020."]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mediterr. J. Math."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s00009-024-02667-4","type":"journal-article","created":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T16:01:21Z","timestamp":1716134481000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Towards the Classification of Semistable Fibrations Having Exactly Five Singular Fibers"],"prefix":"10.1007","volume":"21","author":[{"given":"Margarita","family":"Casta\u00f1eda-Salazar","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8921-291X","authenticated-orcid":false,"given":"Margarida","family":"Mendes Lopes","sequence":"additional","affiliation":[]},{"given":"Alexis","family":"Zamora","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,19]]},"reference":[{"key":"2667_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s13348-010-0001-0","volume":"62","author":"CR Alc\u00e1ntara","year":"2011","unstructured":"Alc\u00e1ntara, C.R., Castorena, A., Zamora, A.G.: On the slope of relatively minimal fibrations on complex rational surfaces. Collect. Math. 62, 1\u201315 (2011)","journal-title":"Collect. Math."},{"key":"2667_CR2","unstructured":"Beauville, A.: Le nombre minimum de fibres singuli\u00e9res d\u2019une courbe stable sur $$\\mathbb{P} ^1$$. Ast\u00e9risque 86, 97\u2013108 (1981)"},{"key":"2667_CR3","unstructured":"Beauville, A. Le.: Les families stables de courbes elliptiques sur $$\\mathbb{P} ^{1}$$ admettant quatre fibres singuli\u00e9res. C. R. Acad. Sci. Paris 294, 657\u2013660 (1982)"},{"key":"2667_CR4","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/s40590-017-0185-3","volume":"25","author":"M Casta\u00f1eda","year":"2019","unstructured":"Casta\u00f1eda, M., Zamora, A.G.: Semistable fibrations over $$\\mathbb{P} ^1$$ with five singular fibers. Bol. Soc. Mat. Mex. 25, 13\u201319 (2019)","journal-title":"Bol. Soc. Mat. Mex."},{"key":"2667_CR5","doi-asserted-by":"crossref","unstructured":"Dolgachev, I.: Classical algebraic geometry. A modern view. Cambridge: Cambridge University Press, xii, p. 639 (2012)","DOI":"10.1017\/CBO9781139084437"},{"key":"2667_CR6","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1007\/s40879-018-0231-3","volume":"4","author":"I Dolgachev","year":"2018","unstructured":"Dolgachev, I., Farb, B., Looijenga, E.: Geometry of the Wiman-Edge pencil, I: algebro-geometric aspects. Eur. J. Math. 4, 879\u2013930 (2018)","journal-title":"Eur. J. Math."},{"key":"2667_CR7","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1017\/S0305004100058321","volume":"89","author":"WL Edge","year":"1981","unstructured":"Edge, W.L.: A pencil of four-nodal plane sextics. Math. Proc. Camb. Philos. Soc. 89, 413\u2013421 (1981)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"2667_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-023-01841-2","author":"L Gui-Min","year":"2023","unstructured":"Gui-Min, L., Wan-Yuan, X., Hui-Ting, Z.: A remark on a conjecture of Tan. Monatshefte f\u00fcr Mathematik (2023). https:\/\/doi.org\/10.1007\/s00605-023-01841-2","journal-title":"Monatshefte f\u00fcr Mathematik"},{"issue":"4","key":"2667_CR9","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1070\/IM2002v066n04ABEH000397","volume":"66","author":"NV Khac","year":"2002","unstructured":"Khac, N.V., Saito, M.-H.: On Mordell-Weil lattices for non-hyperelliptic fibrations on surfaces with zero geometric genus and irregularity. Izv. Math. 66(4), 789\u2013805 (2002)","journal-title":"Izv. Math."},{"issue":"1","key":"2667_CR10","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s00209-005-0797-6","volume":"251","author":"S Kitagawa","year":"2005","unstructured":"Kitagawa, S., Konno, K.: Fibred rational surfaces with extremal Mordell\u2013Weil lattices. Math. Z. 251(1), 179\u2013204 (2005)","journal-title":"Math. Z."},{"key":"2667_CR11","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1007\/s00208-017-1528-0","volume":"370","author":"X Lu","year":"2018","unstructured":"Lu, X., Tan, S.-L., Zuo, K.: Singular fibers and Kodaira dimensions. Math. Ann. 370, 1717\u20131728 (2018)","journal-title":"Math. Ann."},{"key":"2667_CR12","doi-asserted-by":"crossref","unstructured":"Nagata, M.: On rational surfaces I. Memoirs of the College of Science, University of Kyoto, Series A, Vol. XXXII, pp. 351\u2013370 (1960)","DOI":"10.1215\/kjm\/1250775912"},{"issue":"2","key":"2667_CR13","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1016\/j.aim.2008.05.014","volume":"219","author":"JV Pereira","year":"2008","unstructured":"Pereira, J.V., Yuzvinsky, S.: Completely reducible hypersurfaces in a pencil. Adv. Math. 219(2), 672\u2013688 (2008)","journal-title":"Adv. Math."},{"key":"2667_CR14","doi-asserted-by":"crossref","unstructured":"Reid, M.: Chapters on algebraic surfaces. In: Koll\u00e1r, J. (ed.) Complex Algebraic Geometry, IAS\/Park City Math. Ser. 3, pp. 3\u2013159. Amer. Math. Soc., Providence (1997)","DOI":"10.1090\/pcms\/003\/02"},{"key":"2667_CR15","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s00209-004-0706-4","volume":"249","author":"S-L Tan","year":"2005","unstructured":"Tan, S.-L., Tu, Y., Zamora, A.G.: On complex surfaces with 5 or 6 semistable singular fibers over $$\\mathbb{P} ^1$$. Math. Z. 249, 427\u2013438 (2005)","journal-title":"Math. Z."},{"key":"2667_CR16","first-page":"591","volume":"4","author":"S-L Tan","year":"1995","unstructured":"Tan, S.-L.: The minimal number of singular fibers of a semistable curve over $$\\mathbb{P} ^1$$. J. Algebraic Geom. 4, 591\u2013596 (1995)","journal-title":"J. Algebraic Geom."},{"key":"2667_CR17","unstructured":"Vojta, P.: Diophantine Inequalities and Arakelov Theory, pp. 155\u2013178. Appendix to introduction to Arakelov theory by S. Lan, Springer-Verlag (1988)"},{"key":"2667_CR18","unstructured":"Yu, F.: On the minimal number of singular fibers of semi-stable pencils. Ph.D. Thesis, East China Normal University (2008)"},{"key":"2667_CR19","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1017\/S0013091517000232","volume":"61","author":"AG Zamora","year":"2018","unstructured":"Zamora, A.G.: Some remarks on the Wiman\u2013Edge pencil. Proceedings of the Edinburgh Mathematical Society 61, 401\u2013412 (2018)","journal-title":"Proceedings of the Edinburgh Mathematical Society"}],"container-title":["Mediterranean Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-024-02667-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00009-024-02667-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-024-02667-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T14:12:54Z","timestamp":1718979174000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00009-024-02667-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,19]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2667"],"URL":"https:\/\/doi.org\/10.1007\/s00009-024-02667-4","relation":{},"ISSN":["1660-5446","1660-5454"],"issn-type":[{"value":"1660-5446","type":"print"},{"value":"1660-5454","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,19]]},"assertion":[{"value":"26 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"125"}}