The Aluffi algebra of the Jacobian of points in projective space: Torsion-freeness

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• 作者：Abbas Nasrollah Nejad^a ; ^b ; ¹ ; ^{abbasnn@iasbs.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Aron Simis^c ; ^d ; ² ; ^{aron@dmat.ufpe.br" class="auth_mail" title="E-mail the corresponding author} ; Rashid Zaare-Nahandi^a ; ^{rashidzn@iasbs.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13A30 ; 13C12 ; 13C40 ; secondary ; 14M12 ; 14C17
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：467
• 期：Complete
• 页码：268-283
• 全文大小：369 K

文摘

The algebra in the title has been introduced by P. Aluffi. Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si1.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=8e7576fb8db46b57269cbe2b60722299" title="Click to view the MathML source">J⊂Iclass="mathContainer hidden">class="mathCode">$J\subset I$ be ideals in the commutative ring R. The (embedded) Aluffi algebra of I   on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si2.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=6f0c50d820d1251431af2c3aa21e1d31" title="Click to view the MathML source">R/Jclass="mathContainer hidden">class="mathCode">$R/J$ is an intermediate graded algebra between the symmetric algebra and Rees Algebra of the ideal class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si3.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=f3cd88e3071805c5a6af709606bec830" title="Click to view the MathML source">I/Jclass="mathContainer hidden">class="mathCode">$I/J$ over class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si2.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=6f0c50d820d1251431af2c3aa21e1d31" title="Click to view the MathML source">R/Jclass="mathContainer hidden">class="mathCode">$R/J$. A pair of ideals has been dubbed an Aluffi torsion-free pair if the surjective map of the Aluffi algebra of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si3.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=f3cd88e3071805c5a6af709606bec830" title="Click to view the MathML source">I/Jclass="mathContainer hidden">class="mathCode">$I/J$ onto the Rees algebra of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302587&_mathId=si3.gif&_user=111111111&_pii=S0021869316302587&_rdoc=1&_issn=00218693&md5=f3cd88e3071805c5a6af709606bec830" title="Click to view the MathML source">I/Jclass="mathContainer hidden">class="mathCode">$I/J$ is injective. In this paper we focus on the situation where J is the ideal of points in general linear position in projective space and I is its Jacobian ideal.