Construction algorithms for rational cubic surfaces

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• 作者：Jon Gonzá ; lez-Sá ; nchez^a ; ¹ ; ^{jon.gonzalez@ehu.es" class="auth_mail" title="E-mail the corresponding author} ; Irene Polo-Blanco^b ; ² ; ^{irene.polo@unican.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Del Pezzo ; Rational surface ; Cubic surface ; Parametrization ; Algorithm
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P2
• 页码：309-326
• 全文大小：612 K

文摘

By a criterion of Swinnerton-Dyer it is known that a smooth cubic surface S   defined over n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000195&_mathId=si1.gif&_user=111111111&_pii=S0747717116000195&_rdoc=1&_issn=07477171&md5=70031df267d4376217ea9f3fa3d40f52" title="Click to view the MathML source">Qn>n class="mathContainer hidden">n class="mathCode">n>n>n> is birationally trivial over n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000195&_mathId=si1.gif&_user=111111111&_pii=S0747717116000195&_rdoc=1&_issn=07477171&md5=70031df267d4376217ea9f3fa3d40f52" title="Click to view the MathML source">Qn>n class="mathContainer hidden">n class="mathCode">n>n>n> if and only if n id="mmlsi2" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000195&_mathId=si2.gif&_user=111111111&_pii=S0747717116000195&_rdoc=1&_issn=07477171&md5=ca474ff5c1c53a51d1ac175a7ba83af6" title="Click to view the MathML source">S(Q)&ne;∅n>n class="mathContainer hidden">n class="mathCode">n>n>n> and S   contains a n id="mmlsi10" class="mathmlsrc">nce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000195&_mathId=si10.gif&_user=111111111&_pii=S0747717116000195&_rdoc=1&_issn=07477171&md5=c87776ffccbafe864380b1970ee078a8">nlineImage" height="16" width="59" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0747717116000195-si10.gif"><noscript>n:bottom" width="59" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0747717116000195-si10.gif">noscript>n class="mathContainer hidden">n class="mathCode">n>n>n>-stable set of 2, 3 or 6 skew lines. In this text we describe birationally trivial smooth cubic surfaces over n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000195&_mathId=si1.gif&_user=111111111&_pii=S0747717116000195&_rdoc=1&_issn=07477171&md5=70031df267d4376217ea9f3fa3d40f52" title="Click to view the MathML source">Qn>n class="mathContainer hidden">n class="mathCode">n>n>n> and provide algorithms to construct explicit cubic surfaces for each of the cases in Swinnerton-Dyer's criterion.