On Segre's bound for fat points in

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• 作者：Edoardo Ballico^a ; ^{ballico@science.unitn.it" class="auth_mail" title="E-mail the corresponding author} ; Olivia Dumitrescu^b ; ^{dumitrescu@math.uni-hannover.de" class="auth_mail" title="E-mail the corresponding author} ; Elisa Postinghel^c ; ^{elisa.postinghel@wis.kuleuven.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 13D40 ; secondary ; 14C20
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：220
• 期：6
• 页码：2307-2323
• 全文大小：485 K

文摘

For a scheme of fat points Z   defined by the saturated ideal class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si2.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=3d0964548f0bd191d45aebdb75ed296a" title="Click to view the MathML source">I_Zclass="mathContainer hidden">class="mathCode">${\mathcal{I}}_Z$, the regularity index computes the Castelnuovo–Mumford regularity of the Cohen–Macaulay ring class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si3.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=e33a350ef50fb2f1c572eafcf4cbb350" title="Click to view the MathML source">R/I_Zclass="mathContainer hidden">class="mathCode">$R/{\mathcal{I}}_Z$. For points in “general position” we improve the bound for the regularity index computed by Segre for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si24.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=6337d0cb59896f4d84b120002bf8e496" title="Click to view the MathML source">P²class="mathContainer hidden">class="mathCode">${\mathbb{P}}^2$ and generalised by Catalisano, Trung and Valla for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si1.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=095f959a153b512e7b5d93153704788f" title="Click to view the MathML source">Pⁿclass="mathContainer hidden">class="mathCode">${\mathbb{P}}^n$. Moreover, we prove that the generalised Segre's bound conjectured by Fatabbi and Lorenzini holds for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si5.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=b01262e947a2de366a7a18893500b016" title="Click to view the MathML source">n+3class="mathContainer hidden">class="mathCode">$n+3$ arbitrary points in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003242&_mathId=si1.gif&_user=111111111&_pii=S0022404915003242&_rdoc=1&_issn=00224049&md5=095f959a153b512e7b5d93153704788f" title="Click to view the MathML source">Pⁿclass="mathContainer hidden">class="mathCode">${\mathbb{P}}^n$. We propose a modification of Segre's conjecture for arbitrary points and we discuss some evidences.