{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:27:54Z","timestamp":1759134474666},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p> Given a [Formula: see text]-dimensional vector subspace [Formula: see text] of [Formula: see text], a tensor product surface, denoted by [Formula: see text], is the closure of the image of the rational map [Formula: see text] determined by [Formula: see text]. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of [Formula: see text] in [Formula: see text]. In this paper, we show that if [Formula: see text] has a finite set of [Formula: see text] basepoints in generic position, then the implicit equation of [Formula: see text] is determined by two syzygies of [Formula: see text] in bidegrees [Formula: see text] and [Formula: see text]. This result is proved by understanding the geometry of the basepoints of [Formula: see text] in [Formula: see text]. The proof techniques for the main theorem also apply when [Formula: see text] is basepoint free. <\/jats:p>","DOI":"10.1142\/s0219498817501894","type":"journal-article","created":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T06:16:40Z","timestamp":1476857800000},"page":"1750189","source":"Crossref","is-referenced-by-count":0,"title":["Implicitization of tensor product surfaces in the presence of a generic set of basepoints"],"prefix":"10.1142","volume":"16","author":[{"given":"Eliana","family":"Duarte","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,9,20]]},"reference":[{"key":"S0219498817501894BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.09.019"},{"key":"S0219498817501894BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.07.028"},{"key":"S0219498817501894BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2015.09.001"},{"key":"S0219498817501894BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2012.04.002"},{"key":"S0219498817501894BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-33275-6_2"},{"key":"S0219498817501894BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2005.01.003"},{"key":"S0219498817501894BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00012-7"},{"key":"S0219498817501894BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/334\/05979"},{"key":"S0219498817501894BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2007.07.015"},{"key":"S0219498817501894BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/12703"},{"key":"S0219498817501894BIB011","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1992.155.251"},{"key":"S0219498817501894BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24166-1"},{"key":"S0219498817501894BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(82)90034-5"},{"key":"S0219498817501894BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2013-02764-0"},{"key":"S0219498817501894BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00072-5"},{"key":"S0219498817501894BIB017","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610705006459"}],"container-title":["Journal of Algebra and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219498817501894","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:53:38Z","timestamp":1565139218000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219498817501894"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,20]]},"references-count":16,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,9,20]]},"published-print":{"date-parts":[[2017,10]]}},"alternative-id":["10.1142\/S0219498817501894"],"URL":"https:\/\/doi.org\/10.1142\/s0219498817501894","relation":{},"ISSN":["0219-4988","1793-6829"],"issn-type":[{"value":"0219-4988","type":"print"},{"value":"1793-6829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,20]]}}}