The divisor class groups of some rings of holomorphic functions
Identifieur interne : 000E94 ( Istex/Curation ); précédent : 000E93; suivant : 000E95The divisor class groups of some rings of holomorphic functions
Auteurs : David Prill [Suisse]Source :
- Mathematische Zeitschrift [ 0025-5874 ] ; 1971-03-01.
English descriptors
- KwdEn :
- Abelian, Abelian group, Algebraic, Analytic space, Analytic spaces, Canonical mapping, Cech, Cohomology, Cohomology groups, Cohomology sequence, Commutative, Commutative diagram, Compact stein, Countable, Countable stein, Direct limit, Divisor, Divisor class, Divisor class group, Divisor class groups, Exact sequence, Factorization, Finite group, Finitely, First isomorphism, Germ, Holomorphic, Holomorphic function, Holomorphic functions, Homomorphism, Ideal sheaf, Injective, Intersection matrix, Irreducible, Irreducible subvariety, Isomorphism, Lemma, Lira, Local ring, Math, Meromorphic functions, Noetherian, Open neighborhood, Open neighborhoods, Open sets, Open stein neighborhood, Open subsets, Prill, Princeton university press, Quotient, Resp, Sheaf, Singular locus, Singular point, Singularity, Star neighborhood, Stein manifolds, Subset, Subvariety, Surjective, Topological, Topological vector spaces, Topology, Unique factorization domain, Unique factorization domains.
- Teeft :
- Abelian, Abelian group, Algebraic, Analytic space, Analytic spaces, Canonical mapping, Cech, Cohomology, Cohomology groups, Cohomology sequence, Commutative, Commutative diagram, Compact stein, Countable, Countable stein, Direct limit, Divisor, Divisor class, Divisor class group, Divisor class groups, Exact sequence, Factorization, Finite group, Finitely, First isomorphism, Germ, Holomorphic, Holomorphic function, Holomorphic functions, Homomorphism, Ideal sheaf, Injective, Intersection matrix, Irreducible, Irreducible subvariety, Isomorphism, Lemma, Lira, Local ring, Math, Meromorphic functions, Noetherian, Open neighborhood, Open neighborhoods, Open sets, Open stein neighborhood, Open subsets, Prill, Princeton university press, Quotient, Resp, Sheaf, Singular locus, Singular point, Singularity, Star neighborhood, Stein manifolds, Subset, Subvariety, Surjective, Topological, Topological vector spaces, Topology, Unique factorization domain, Unique factorization domains.
Abstract
Abstract: Let (X, x O) be a normal complex analytic space andA⋐X a connected Stein compact set, i.e. a compact subset ofX which has a basis of open neighborhoods which are Stein spaces. We restrict attention to thoseA such thatR=H 0 O) is Noetherian. In Section I various exact sequences involving the divisor class group ofR, denotedC(R), are developed. (IfA is a point, one of these sequences is well-known [24], [39].) LetB be a connected compact Stein set on a normal varietyY such thatS=H o(B, Y O) andT=H o(A×B, X×Y O are Noetherian. In II we give a Künneth-type formula which relatesC(R), C(S) andC(T). In III we show certain analytic local rings are unique factorization domains, study the divisor class groups of local rings on the quotient of an analytic space by a finite group, and prove a simple result on the topology of germs of complex analytic sets. We give a function-theoretic proof that complete intersections of dimensions greater than three which have isolated singularities have local rings which are unique factorization domains.
Url:
DOI: 10.1007/BF01110367
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<term>Analytic spaces</term>
<term>Canonical mapping</term>
<term>Cech</term>
<term>Cohomology</term>
<term>Cohomology groups</term>
<term>Cohomology sequence</term>
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<term>Commutative diagram</term>
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<term>Countable</term>
<term>Countable stein</term>
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<term>Factorization</term>
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<term>Finitely</term>
<term>First isomorphism</term>
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<term>Holomorphic function</term>
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<term>Homomorphism</term>
<term>Ideal sheaf</term>
<term>Injective</term>
<term>Intersection matrix</term>
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<term>Lemma</term>
<term>Lira</term>
<term>Local ring</term>
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<term>Meromorphic functions</term>
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<term>Open subsets</term>
<term>Prill</term>
<term>Princeton university press</term>
<term>Quotient</term>
<term>Resp</term>
<term>Sheaf</term>
<term>Singular locus</term>
<term>Singular point</term>
<term>Singularity</term>
<term>Star neighborhood</term>
<term>Stein manifolds</term>
<term>Subset</term>
<term>Subvariety</term>
<term>Surjective</term>
<term>Topological</term>
<term>Topological vector spaces</term>
<term>Topology</term>
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<term>Unique factorization domains</term>
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<term>Commutative diagram</term>
<term>Compact stein</term>
<term>Countable</term>
<term>Countable stein</term>
<term>Direct limit</term>
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<term>Intersection matrix</term>
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<term>Isomorphism</term>
<term>Lemma</term>
<term>Lira</term>
<term>Local ring</term>
<term>Math</term>
<term>Meromorphic functions</term>
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<term>Open subsets</term>
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<term>Princeton university press</term>
<term>Quotient</term>
<term>Resp</term>
<term>Sheaf</term>
<term>Singular locus</term>
<term>Singular point</term>
<term>Singularity</term>
<term>Star neighborhood</term>
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<term>Subvariety</term>
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<front><div type="abstract" xml:lang="en">Abstract: Let (X, x O) be a normal complex analytic space andA⋐X a connected Stein compact set, i.e. a compact subset ofX which has a basis of open neighborhoods which are Stein spaces. We restrict attention to thoseA such thatR=H 0 O) is Noetherian. In Section I various exact sequences involving the divisor class group ofR, denotedC(R), are developed. (IfA is a point, one of these sequences is well-known [24], [39].) LetB be a connected compact Stein set on a normal varietyY such thatS=H o(B, Y O) andT=H o(A×B, X×Y O are Noetherian. In II we give a Künneth-type formula which relatesC(R), C(S) andC(T). In III we show certain analytic local rings are unique factorization domains, study the divisor class groups of local rings on the quotient of an analytic space by a finite group, and prove a simple result on the topology of germs of complex analytic sets. We give a function-theoretic proof that complete intersections of dimensions greater than three which have isolated singularities have local rings which are unique factorization domains.</div>
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