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  • Produktbild: Equimultiplicity and Blowing Up
  • Produktbild: Equimultiplicity and Blowing Up

Equimultiplicity and Blowing Up An Algebraic Study

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

12.10.2011

Verlag

Springer Berlin

Seitenzahl

629

Maße (L/B/H)

24,4/17/3,6 cm

Gewicht

1114 g

Auflage

Softcover reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-3-642-64803-8

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

12.10.2011

Verlag

Springer Berlin

Seitenzahl

629

Maße (L/B/H)

24,4/17/3,6 cm

Gewicht

1114 g

Auflage

Softcover reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-3-642-64803-8

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Equimultiplicity and Blowing Up
  • Produktbild: Equimultiplicity and Blowing Up
  • I — Review of Multiplicity Theory.-
    1 The multiplicity symbol.-
    2 Hilbert functions.-
    3 Generalized multiplicities and Hilbert functions.-
    4 Reductions and integral closure of ideals.-
    5 Faithfully flat extensions.-
    6 Projection formula and criterion for multiplicity one.-
    7 Examples.- II — Z-Graded Rings and Modules.-
    8 Associated graded rings and Rees algebras.-
    9 Dimension.-
    10 Homogeneous parameters.-
    11 Regular sequences on graded modules.-
    12 Review on blowing up.-
    13 Standard bases.-
    14 Examples.- Appendix — Homogeneous subrings of a homogeneous ring.- III — Asymptotic Sequences and Quasi-Unmixed Rings.-
    15 Auxiliary results on integral dependence of ideals.-
    16 Associated primes of the integral closure of powers of an ideal.-
    17 Asymptotic sequences.-
    18 Quasi-unmixed rings.-
    19 The theorem of Rees-Böger.- IV — Various Notions of Equimultiple and Permissible Ideals.-
    20 Reinterpretation of the theorem of Rees-Böger.-
    21 Hironaka-Grothendieck homomorphism.-
    22 Projective normal flatness and numerical characterization of permissibility.-
    23 Hierarchy of equimultiplicity and permissibility.-
    24 Open conditions and transitivity properties.- V — Equimultiplicity and Cohen-Macaulay Property of Blowing Up Rings.-
    25 Graded Cohen-Macaulay rings.-
    26 The case of hypersurfaces.-
    27 Transitivity of Cohen-Macaulayness of Rees rings.- Appendix (K. Yamagishi and U. Orbanz) — Homogeneous domains of minimal multiplicity.- VI — Certain Inequalities and Equalities of Hilbert Functions and Multiplicities.-
    28 Hyperplane sections.-
    29 Quadratic transformations.-
    30 Semicontinuity.-
    31 Permissibility and blowing up of ideals.-
    32 Transversal ideals and flat families.- VII — Local Cohomology and Duality of Graded Rings.-
    33 Review on graded modules.-
    34 Matlis duality.- I: Local case.- II: Graded case.-
    35 Local cohomology.-
    36 Local duality for graded rings.- Appendix — Characterization of local Gorenstein-rings by its injective dimension.- VIII — Generalized Cohen-Macaulay Rings and Blowing Up.-
    37 Finiteness of local cohomology.-
    38 Standard system of parameters.-
    39 The computation of local cohomology of generalized Cohen-Macaulay rings.-
    40 Blowing up of a standard system of parameters.-
    41 Standard ideals on Buchsbaum rings.-
    42 Examples.- IX — Applications of Local Cohomology to the Cohen-Macaulay Behaviour of Blowing Up Rings.-
    43 Generalized Cohen-Macaulay rings with respect to an ideal.-
    44 The Cohen-Macaulay property of Rees algebras.-
    45 Rees algebras of m-primary ideals.-
    46 The Rees algebra of parameter ideals.-
    47 The Rees algebra of powers of parameter ideals.-
    48 Applications to rings of low multiplicity.- Examples.- Appendix (B. Moonen) — Geometric Equimultiplicity.- I. Local Complex Analytic Geometry.-
    1. Local analytic algebras.- 1.1. Formal power series.- 1.2. Convergent power series.- 1.3. Local analytic k-algebras.-
    2. Local Weierstraß Theory I: The Division Theorem.- 2.1. Ordering the monomials.- 2.2. Monomial ideals and leitideals.- 2.3. The Division Theorem.- 2.4. Division with respect to an ideal; standard bases.- 2.5. Applications of standard bases: the General Weierstraß Preparation Theorem and the Krull Intersection Theorem.- 2.6. The classical Weierstraß Theorems.-
    3. Complex spaces and the Equivalence Theorem.- 3.1. Complex spaces.- 3.3. The Equivalence Theorem.- 3.4. The analytic spectrum.-
    4. Local Weierstraß Theory II: Finite morphisms.- 4.1. Finite morphisms.- 4.2. Weierstraß maps.- 4.3. The Finite Mapping Theorem.- 4.4. The Integrality Theorem.-
    5. Dimension and Nullstellensatz.- 5.1. Local dimension.- 5.2. Active elements and the Active Lemma.- 5.3. The Rückert Nullstellensatz.- 5.4. Analytic sets and local decomposition.-
    6. The Local Representation Theorem for comple space-germs (Noether normalization).- 6.1. Openness and dimension.- 6.2. Geometric interpretation of the local dimension and of a system of parameters; algebraic Noether normalization.- 6.3. The Local Representation Theorem; geometric Noether normalization.-
    7. Coherence.- 7.1. Coherent sheaves.- 7.2. Nonzerodivisors.- 7.3. Purity of dimension and local decomposition.- 7.4. Reduction.- II. Geometric Multiplicity.-
    1. Compact Stein neighbourhoods.- 1.1. Coherent sheaves on closed subsets.- 1.2. Stein subsets.- 1.3. Compact Stein subsets and the Flatness Theorem.- 1.4. Existence of compact Stein neighbourhoods.-
    2. Local mapping degree.- 2.1. Local decomposition revisited.- 2.2. Local mapping degree.-
    3. Geometric multiplicity.- 3.1. The tangent cone.- 3.2. Multiplicity.-
    4. The geometry of Samuel multiplicity.- 4.1. Degree of a projective variety.- 4.2. Hilbert functions.- 4.3. A generalization.- 4.4. Samuel multiplicity.-
    5. Algebraic multiplicity.- 5.1. Algebraic degree.- 5.2. Algebraic multiplicity.- III. Geometric Equimultiplicity.-
    1. Normal flatness and pseudoflatness.- 1.1. Generalities from Complex Analytic Geometry.- 1.2. The analytic and projective analytic spectrum.- 1.3. Flatness of admissible graded algebras.- 1.4 The normal cone, normal flatness, and normal pseudoflatness.-
    2. Geometric equimultiplicity along a smooth subspace.- 2.1. Zariski equimultiplicity.- 2.2. The Hironaka-Schickhoff Theorem.-
    3. Geometric equimultiplicity along a general subspace.- 3.1. Zariski equimultiplicity.- 3.2. Normal pseudoflatness.- References.- References — Chapter I.- References — Chapter II.- References — Appendix Chapter II.- References — Chapter III.- References — Chapter IV.- References — Chapter V.- References — Appendix Chapter V.- References — Chapter VI.- References — Chapter VII.- References — Chapter VIII.- References — Chapter IX.- Bibliography to the Appendix Geometric Equimultiplicity.- General Index.