Quasi-one-fibered ideals in two-dimensional Muhly local domains

On the degree function coefficient of a simple complete ideal in dimension two

“…In the first part of Remark 3.5 in [1] this result was erroneously presented as a consequence of Proposition 3.4 of that paper. To correct this we show how the above result can be obtained from [1,Propopsition 3.3]. For definitions and background information the reader is referred to [1].…”

“…T (I) ⊆ {v M , w} with w ∈ T (I) (see [1,Proposition 1.5]). Here T (I) denotes the set of Rees valuations of I.…”

“…To correct this we show how the above result can be obtained from [1,Propopsition 3.3]. For definitions and background information the reader is referred to [1].…”

“…is the unique immediate base point of I and the transform I R1 = I ′ M1 is simple and complete. Thus every simple complete M-primary ideal I of R is quasione-fibered in the sense of Definition 1.7 in [1].…”

Quasi-one-fibered and projectively full ideals in 2-dimensional Muhly rational singularities

“…This implies that m has ord R as unique Rees valuation and that B m R is a desingularization of R [6, p. 403], [8, p. 259]. Here B m R denotes the scheme Proj n 0 m n obtained by blowing up m. Following Debremaeker in [5], an m-primary ideal with exactly one Rees valuation v = ord R is called quasione-fibered. In Sect.…”