The blow-up of a simple ideal

详细信息    查看全文

• 作者：S. Greco^a ; ¹ ; ^{silvio.greco@polito.it" class="auth_mail" title="E-mail the corresponding author} ; K. Kiyek^b ; ^{karlh@math.upb.de" class="auth_mail" title="E-mail the corresponding author} ; J. Soto^c ; ^{soto@us.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 13H05 ; 14J17 ; secondary ; 13J26 ; 14J25
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：220
• 期：3
• 页码：926-943
• 全文大小：566 K

文摘

Let R   be a two-dimensional regular local ring with maximal ideal m$\mathfrak{m}$ and infinite residue field and let I   be a complete simple m$\mathfrak{m}$-primary residually rational ideal of R  ; let Σ=Bl_I(R)$\mathrm{\Sigma }={\mathrm{Bl}}_I(R)$ be the blow-up of I  , and a07859caeb66a6df6f4b5bf9" title="Click to view the MathML source">R=:R₀⊂R₁⊂⋯⊂R_n$R=:R_0\subset R_1\subset \cdots \subset R_n$ be the sequence determined by I  ; R_i$R_i$ is a quadratic transform of R_i−1$R_{i-1}$. Σ is a normal surface; we show that Σ has one resp. two singular points if 34a9ccb5e4283a84" title="Click to view the MathML source">R_n$R_n$ is free resp. not free. The singular points are rational singularities; we determine their multiplicities.