An analogue of Oka’s theorem for weakly normal complex spaces

Adkins, William A.; Andreotti, Aldo; Leahy, John

doi:10.2140/pjm.1977.68.297

Cited by 8 publications

(18 citation statements)

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“…Since ΓX I: X X A 1 -+ X X A 1 is a closed mapping and Γ 9 = 7r X lCΓ^) we see that Γ p is closed in X X A\ We now give some criteria for determining when a union of weakly normal varieties is again weakly normal. The first result (2.18) is based on a Mayer-Vietoris sequence for ideals in a ring and is proven for complex spaces in [2]. Proposition (2.19) generalizes that result.…”

Section: Let X Be a Variety A K-υalued Function φ On X Is Cregular Imentioning

confidence: 78%

“…We include criterion (4) here as it is the most manageable in actual computations. We include the proof of Gilmer and Heitmann for (2) implies (1 We now prove a sequence of results that enable us to obtain refinements of Traverso's structure theorem and its consequence (cf. [20], Theorems 2.1 and 2.3).…”

Section: Is a Local Rings With Maximal Ideal R(b) And The Canonical Mmentioning

confidence: 99%

“…For let p be an arbitrary prime in A and suppose P λ and P 2 Thus every maximal ideal containing P t also contains P 2 and hence P 2 c P λ . Similarly, P, C P 2 so that P x = P 2 .…”

Section: Let π:Y-> X Be a Dominating Finite Morphism Of Irreducible Vmentioning

confidence: 99%

“…Since if <p: V-> C is c-regular then its graph Γ ψ is Z-closed in V X C and hence Γ 9 is an analytic subset of V X C so that ψ is c-holomorphic on V (see [2], Remark 1.4) and φ\ υ is c-holomorphic on U.…”

Section: γ(Vθ X )->γ(U(9< Xh )mentioning

confidence: 99%

“…On a complex space X define the sheaf of c-holomorphic functions Θ ) consist of all continuous complex valued functions on U which are holomorphic at the regular points of U. X is weakly normal if Θ x = Θ pletely classifies weakly normal spaces which are pure dimensional, local complete intersections (cf. [1]). Within the class of weakly normal spaces there is the subclass of locally optimal spaces; these spaces can be described by requiring that a certain local cohomology sheaf be identically zero.…”

Section: Introductionmentioning

confidence: 99%

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Seminormal rings and weakly normal varieties

Leahy¹,

Vitulli²

1981

Nagoya Mathematical Journal

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In the late sixties and early seventies the operation of weak normalization was formally introduced first in the case of analytic spaces and later in the abstract scheme setting (cf. [6] & [4]). The notion arose from a classification problem. An unfortunate phenomenon in this area occurs when one tries to parametrize algebraic objects associated with a space by an algebraic variety; the resulting variety is, in general, not uniquely determined and may, for example, depend on the choice of coordinates. Under certain conditions one does know that the normalization of the parameter variety is unique. The price one pays for passing to the normalization is that often this variety no longer parametrizes what it was intended to; one point on the original parameter variety may split into several in the normalization. This problem is avoided if one passes instead to the weak normalization of the original variety. One then obtains a variety homeomorphic to the original variety with universal mapping properties that guarantee uniqueness.

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Section: Let X Be a Variety A K-υalued Function φ On X Is Cregular Imentioning

confidence: 78%

Section: Is a Local Rings With Maximal Ideal R(b) And The Canonical Mmentioning

confidence: 99%

“…For let p be an arbitrary prime in A and suppose P λ and P 2 Thus every maximal ideal containing P t also contains P 2 and hence P 2 c P λ . Similarly, P, C P 2 so that P x = P 2 .…”

Section: Let π:Y-> X Be a Dominating Finite Morphism Of Irreducible Vmentioning

confidence: 99%

Section: γ(Vθ X )->γ(U(9< Xh )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations