University of Paderborn Department of Mathematics Diploma Thesis ...

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”Im großen Garten der Geometriekann sich jeder nach seinem Geschmackeinen Strauß pflücken.“David Hilbert (23.01.1862 - 14.02.1943)
Page 1: University of PaderbornDepartment o
Page 7: AcknowledgementI would like to than
Page 11 and 12: ContentsIntroduction 31 Notations a
Page 13 and 14: IntroductionThe main result of this
Page 15 and 16: prove that all saturated stable ide
Page 17 and 18: Chapter 1Notations and Prerequisite
Page 19 and 20: 1.1. GENERAL PREREQUISITES AND TERM
Page 21 and 22: 1.2. HILBERT FUNCTION, HILBERT POLY
Page 23 and 24: 1.2. HILBERT FUNCTION, HILBERT POLY
Page 25 and 26: 1.3. CHARACTERIZATION OF HILBERT FU
Page 27 and 28: 1.3. CHARACTERIZATION OF HILBERT FU
Page 29 and 30: Chapter 2Stable idealsIn this chapt
Page 31 and 32: 2.2. STABILITY OF BOREL-FIXED IDEAL
Page 33 and 34: 2.2. STABILITY OF BOREL-FIXED IDEAL
Page 35 and 36: 2.3. SATURATION OF STABLE IDEALS 25
Page 37 and 38: 2.4. HILBERT SERIES OF STABLE IDEAL
Page 39 and 40: 2.4. HILBERT SERIES OF STABLE IDEAL
Page 41 and 42: 2.5. A LINK BETWEEN HILBERT SERIES
Page 43 and 44: 2.5. A LINK BETWEEN HILBERT SERIES
Page 45 and 46: 2.6. A LINK BETWEEN HILBERT POLYNOM
Page 47 and 48: 2.6. A LINK BETWEEN HILBERT POLYNOM
Page 49 and 50: 2.7. HILBERT POLYNOMIALS OF STABLE
Page 51 and 52: 2.8. AN APPLICATION TO GOTZMANN’S
Page 53 and 54: 2.8. AN APPLICATION TO GOTZMANN’S
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Chapter 3Operations on stable ideal
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3.2. EXPANSIONS AND CONTRACTIONS OF
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3.3. STABLE IDEALS WITH THE SAME DO
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3.4. STABLE IDEALS WITH THE SAME HI
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3.4. STABLE IDEALS WITH THE SAME HI
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Chapter 4Algorithms for stable idea
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4.1. COMPUTING HILBERT SERIES OF ST
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4.2. COMPUTING HILBERT POLYNOMIALS
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4.2. COMPUTING HILBERT POLYNOMIALS
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4.3. COMPUTING THE LEXICOGRAPHIC ID
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4.3. COMPUTING THE LEXICOGRAPHIC ID
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4.4. COMPUTING EXPANSIONS AND CONTR
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4.5. COMPUTING STABLE IDEALS TO A G
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4.6. COMPUTING ALL HILBERT SERIES T
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4.6. COMPUTING ALL HILBERT SERIES T
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4.7. COMPUTING ALL HILBERT FUNCTION
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4.7. COMPUTING ALL HILBERT FUNCTION
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4.8. SOME CONCLUSIONS AND EXPERIMEN
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4.8. SOME CONCLUSIONS AND EXPERIMEN
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λ weight order with weight functio
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Bibliography[1] D. Bayer, The divis
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University of Paderborn Department of Mathematics Diploma Thesis ...

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