{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T17:56:25Z","timestamp":1781286985923,"version":"3.54.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2007,5]]},"abstract":"<jats:p> This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces F<jats:sub>k<\/jats:sub>(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is [Formula: see text] where c = gcd (a, b) and n = 2ab + kb<jats:sup>2<\/jats:sup>. In this paper, we degenerate the Hirzebruch surface F<jats:sub>1<\/jats:sub>(2, 2), compute the braid monodromy factorization of the branch curve in \u2102<jats:sup>2<\/jats:sup>, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F<jats:sub>1<\/jats:sub>(2, 2) with respect to a generic projection is isomorphic to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196707003780","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T11:38:28Z","timestamp":1180525108000},"page":"507-525","source":"Crossref","is-referenced-by-count":5,"title":["THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F<sub>1<\/sub>(2, 2)"],"prefix":"10.1142","volume":"17","author":[{"given":"MEIRAV","family":"AMRAM","sequence":"first","affiliation":[{"name":"Einstein Institute for Mathematics, Hebrew University, Jerusalem, Israel"},{"name":"Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MINA","family":"TEICHER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"UZI","family":"VISHNE","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2002.2.403"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022396230382"},{"key":"rf6","first-page":"1","volume":"40","author":"Amram M.","journal-title":"Osaka J. Math."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/00927870500346024"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.top.2004.01.006"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01343552"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388987"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/078\/975093"},{"key":"rf14","series-title":"Lecture Notes in Mathematics","volume-title":"Algebraic Geometry","volume":"1479","author":"Moishezon B.","year":"1990"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01444235"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/162\/01540"},{"key":"rf17","unstructured":"B.\u00a0Moishezon and M.\u00a0Teicher, Classification of Algebraic Varieties, Contemporary Mathematics\u00a0162 (Amer. Math. Soc., Providence, RI, 1994)\u00a0pp. 332\u2013358."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.4310\/CAG.1996.v4.n1.a1"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/241\/03642"},{"key":"rf20","first-page":"139","volume":"8","author":"Rowen L. H.","journal-title":"J. Group Theory"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196707003780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:42:24Z","timestamp":1565185344000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196707003780"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5]]},"references-count":15,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,5]]}},"alternative-id":["10.1142\/S0218196707003780"],"URL":"https:\/\/doi.org\/10.1142\/s0218196707003780","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5]]}}}