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 d0964548f0bd191d45aebdb75ed296a" title="Click to view the MathML source">I_Z${\mathcal{I}}_Z$, the regularity index computes the Castelnuovo–Mumford regularity of the Cohen–Macaulay ring R/I_Z$R/{\mathcal{I}}_Z$. For points in “general position” we improve the bound for the regularity index computed by Segre for P²${\mathbb{P}}^2$ and generalised by Catalisano, Trung and Valla for Pⁿ${\mathbb{P}}^n$. Moreover, we prove that the generalised Segre's bound conjectured by Fatabbi and Lorenzini holds for n+3$n+3$ arbitrary points in Pⁿ${\mathbb{P}}^n$. We propose a modification of Segre's conjecture for arbitrary points and we discuss some evidences.