Classification of Two-Dimensional F-Regular and F-Pure Singularities
نویسندگان
چکیده
منابع مشابه
F-pure Thresholds and F-jumping Exponents in Dimension Two
Using an argument based on an idea of Monsky, we prove the rationality of the F-pure thresholds of curve singularities on a smooth surface defined over a finite field. More generally, we prove in this setting the rationality and discreteness of F-jumping exponents, the smallest positive one of which is the F-pure threshold. We also give a lower bound for F-pure thresholds in the homogeneous case.
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چکیده ندارد.
15 صفحه اولThe Monotonicity of the F-blowup Sequence of F-pure Singularities
Recently the author defined a sequence of blowups for each variety in positive characteristic, called F-blowups. Our purpose is to prove that the sequence is monotone if the variety has only F-pure singularities. As a corollary, we also obtain some result on the stability of the sequence.
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We discuss Matijevic–Roberts type theorem on strong F -regularity, F -purity, and Cohen–Macaulay F -injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F -purity of homomorphisms using Radu–André homomorphisms, and prove basic properties of it. We also discuss a...
متن کاملOn F-pure Thresholds
Using the Frobenius map, we introduce a new invariant for a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes several ring theoretic properties. By virtue of Hara and Yoshida’s result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1998
ISSN: 0001-8708
DOI: 10.1006/aima.1997.1682