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  1. Bulletin of the Brazilian Mathematical Society
  2. Bulletin of the Brazilian Mathematical Society : Volume 45
  3. Bulletin of the Brazilian Mathematical Society : Volume 45, Issue 4, December 2014
  4. Integrality in codimension one
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Bulletin of the Brazilian Mathematical Society : Volume 48
Bulletin of the Brazilian Mathematical Society : Volume 47
Bulletin of the Brazilian Mathematical Society : Volume 46
Bulletin of the Brazilian Mathematical Society : Volume 45
Bulletin of the Brazilian Mathematical Society : Volume 45, Issue 4, December 2014
Complete intersections in certain affine and projective monomial curves
Computing Severi degrees with long-edge graphs
Gonality of non-Gorenstein curves of genus five
A note on Gorenstein monomial curves
The first Euler characteristics versus the homological degrees
Strata of vector spaces of forms in R = k[x, y], and of rational curves in ℙ k
Betti numbers associated to the facet ideal of a matroid
On the tangentially degenerate curves, II
Steenbrink vanishing extended
The F-pure threshold of a determinantal ideal
Regularity and algebraic properties of certain lattice ideals
A simple characteristic-free proof of the Brill-Noether theorem
Plane quartics with at least 8 hyperinflection points
Degree of the variety of pairs of nilpotent commuting matrices
Integrality in codimension one
On the radical of endomorphism rings of local modules
Classification of 2-dimensional graded normal hypersurfaces with a(R) ≤ 6
Bulletin of the Brazilian Mathematical Society : Volume 45, Issue 3, September 2014
Bulletin of the Brazilian Mathematical Society : Volume 45, Issue 2, June 2014
Bulletin of the Brazilian Mathematical Society : Volume 45, Issue 1, March 2014
Bulletin of the Brazilian Mathematical Society : Volume 44
Bulletin of the Brazilian Mathematical Society : Volume 43
Bulletin of the Brazilian Mathematical Society : Volume 42
Bulletin of the Brazilian Mathematical Society : Volume 41
Bulletin of the Brazilian Mathematical Society : Volume 40
Bulletin of the Brazilian Mathematical Society : Volume 39
Bulletin of the Brazilian Mathematical Society : Volume 38
Bulletin of the Brazilian Mathematical Society : Volume 37
Bulletin of the Brazilian Mathematical Society : Volume 36
Bulletin of the Brazilian Mathematical Society : Volume 35
Bulletin of the Brazilian Mathematical Society : Volume 34
Bulletin of the Brazilian Mathematical Society : Volume 33
Bulletin of the Brazilian Mathematical Society : Volume 32
Bulletin of the Brazilian Mathematical Society : Volume 31
Bulletin of the Brazilian Mathematical Society : Volume 30
Bulletin of the Brazilian Mathematical Society : Volume 29
Bulletin of the Brazilian Mathematical Society : Volume 28

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Integrality in codimension one

Content Provider Springer Nature Link
Author Thorup, Anders
Copyright Year 2014
Abstract The paper from 2001 by Simis, Ulrich, and Vasconcelos contained deep results on codimension, multiplicity and integral extensions. The results and the ideas of the paper led to substantial simplifications in the treatment of the exceptional fiber of a conormal space, considered previously by Kleiman and the present author. In addition, the paper contained the following theorem: Let R ⊆ S be an extension of commutative rings, where R is noetherian, universally catenary, and locally equidimensional. Then the extension R ⊆ S is integral if minimal primes of S contract to minimal primes of R and, for every prime $$\mathfrak{p}$$ of height at most 1 in R, the extension $$R_\mathfrak{p} \subseteq S_\mathfrak{p}$$ is integral.The main purpose of the present note is to give an alternative proof of the theorem, based on standard techniques of projective geometry. In addition, the results on the exceptional fiber, considered previously by Kleiman and the present author in the complex analytic case, may be based in the algebraic case by a simple key result presented at the end.
Ending Page 870
Page Count 6
Starting Page 865
File Format PDF
ISSN 16787544
e-ISSN 16787714
Journal Bulletin of the Brazilian Mathematical Society
Issue Number 4
Volume Number 45
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2015-01-06
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword standard graded algebra Polynomials over commutative rings Theoretical, Mathematical and Computational Physics Mathematics Galois theory integral extension exceptional fiber finite map
Content Type Text
Resource Type Article
Subject Mathematics
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