{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:27:47Z","timestamp":1750220867102,"version":"3.41.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2019,2,16]],"date-time":"2019-02-16T00:00:00Z","timestamp":1550275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2019,2,16]]},"abstract":"<jats:p>\n            Bresinsky defined a class of monomial curves in A\n            <jats:sup>4<\/jats:sup>\n            with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for this class. We also propose a general construction of such curves in arbitrary embedding dimension.\n          <\/jats:p>","DOI":"10.1145\/3313880.3313895","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T20:54:15Z","timestamp":1550609655000},"page":"104-107","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Unboundedness of Betti numbers of curves"],"prefix":"10.1145","volume":"52","author":[{"given":"Ranjana","family":"Mehta","sequence":"first","affiliation":[{"name":"IIT Gandhinagar, Palaj, Gandhinagar, Gujarat, INDIA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joydip","family":"Saha","sequence":"additional","affiliation":[{"name":"IIT Gandhinagar, Palaj, Gandhinagar, Gujarat, INDIA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indranath","family":"Sengupta","sequence":"additional","affiliation":[{"name":"IIT Gandhinagar, Palaj, Gandhinagar, Gujarat, INDIA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,2,16]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"H. Bresinsky On Prime Ideals with Generic Zero x<sub>i<\/sub> = t<sup>ni<\/sup> Proceedings of the American Mathematical Society Vol.47 No.2 february 1975.  H. Bresinsky On Prime Ideals with Generic Zero x<sub>i<\/sub> = t<sup>ni<\/sup> Proceedings of the American Mathematical Society Vol.47 No.2 february 1975.","DOI":"10.2307\/2039739"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01170309"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01303625"},{"key":"e_1_2_1_4_1","unstructured":"W. Decker; G.-M. Greuel; G. Pfister; H. Sch\u00f6nemann: S<scp>ingular<\/scp> 4-1-1 --- A computer algebra system for polynomial computations. http:\/\/www.singular.uni-kl.de (2018).  W. Decker; G.-M. Greuel; G. Pfister; H. Sch\u00f6nemann: S<scp>ingular<\/scp> 4-1-1 --- A computer algebra system for polynomial computations. http:\/\/www.singular.uni-kl.de (2018)."},{"key":"e_1_2_1_5_1","unstructured":"The GAP Group GAP - Groups Algorithms and Programming Version 4.8.6; 2016.  The GAP Group GAP - Groups Algorithms and Programming Version 4.8.6; 2016."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01273309"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/02640722"},{"key":"e_1_2_1_8_1","first-page":"309","volume":"77","author":"Moh T. T.","year":"1979","journal-title":"American Mathematical Society"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-01-05819-1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","unstructured":"J.C.Rosales P.A.Garc\u00eda-S\u00e1nchez Numerical Semigroups Springer (2009).  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