| eBook ISBN: | 978-1-4704-0473-4 |
| Product Code: | MEMO/185/869.E |
| List Price: | $93.00 |
| MAA Member Price: | $83.70 |
| AMS Member Price: | $55.80 |
| eBook ISBN: | 978-1-4704-0473-4 |
| Product Code: | MEMO/185/869.E |
| List Price: | $93.00 |
| MAA Member Price: | $83.70 |
| AMS Member Price: | $55.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 185; 2007; 324 ppMSC: Primary 14; 32; 53
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies.
As another application, the author establishes the correspondence of semisimple regular holonomic \(D\)-modules and polarizable pure imaginary pure twistor \(D\)-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
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Table of Contents
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Chapters
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1. Introduction
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Part 1. Preliminary
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2. Preliminary
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3. Preliminary for mixed twistor structure
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4. Preliminary for filtrations
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5. Some lemmas for generically splitted case
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6. Model bundles
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Part 2. Prolongation of deformed holomorphic bundles
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7. Harmonic bundles on a punctured disc
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8. Harmonic bundles on a product of punctured discs
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9. The KMS-structure of the space of the multi-valued flat sections
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10. The induced regular $\lambda $-connection on $\Delta ^n \times C*$
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Part 3. Limiting mixed twistor theorem and some consequence
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11. The induced vector bundle over $\mathbb {P}^1$
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12. Limiting mixed twistor theorem
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13. Norm estimate
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The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies.
As another application, the author establishes the correspondence of semisimple regular holonomic \(D\)-modules and polarizable pure imaginary pure twistor \(D\)-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
-
Chapters
-
1. Introduction
-
Part 1. Preliminary
-
2. Preliminary
-
3. Preliminary for mixed twistor structure
-
4. Preliminary for filtrations
-
5. Some lemmas for generically splitted case
-
6. Model bundles
-
Part 2. Prolongation of deformed holomorphic bundles
-
7. Harmonic bundles on a punctured disc
-
8. Harmonic bundles on a product of punctured discs
-
9. The KMS-structure of the space of the multi-valued flat sections
-
10. The induced regular $\lambda $-connection on $\Delta ^n \times C*$
-
Part 3. Limiting mixed twistor theorem and some consequence
-
11. The induced vector bundle over $\mathbb {P}^1$
-
12. Limiting mixed twistor theorem
-
13. Norm estimate
