Normal F-pure surface singularities
Normal F-pure surface singularities
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法向 F 纯表面奇点
DOI：
10.1016/0021-8693(91)90255-7
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发表时间：
1991
影响因子：
0.9
通讯作者：
V. Srinivas
中科院分区：
文献类型：
--
作者：
V. Mehta;V. Srinivas
An inclusion of Noetherian local rings R+ S is called pure if for any R-module M, the map A4---f SOR A4 is injective. If S is finitely generated as an R-module, then purity is equivalent to R being a direct summand of S as an R-module. A local ring R in characteristic p is said to be F-pure if the Frobenius map F: R-+ R is pure. This notion first appears in [HR]. The notion that a variety in characteristic p is Frobenius split has also been introduced (see [MR]).Let X be a normal projective surface over an algebraically closed field k of characteristic p> 0. Let PE X be a singular point, with R= Or,,. Let f: Y-+ X be the minimal resolution of the singularity at P. If E is the reduced exceptional divisor, then no irreducible component of E is an exceptional curve of the first kind; ie, if E= Uy= i Ei with each Ei irreducible, then Ei E Pi= Ef 6-2. The graph of E is defined as follows: it has a vertex ri associated to each irreducible component Ej of E and an edge joining ui to uj for each point of intersection of E, and Ej. Put Z= Y xX Spec R, so that f: Z+ Spec R is the minimal resolution of singularities of Spec R. We shall prove the following results:
