Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to pro...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автор: Mochizuki, Takuro
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211355
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Good Wild Harmonic Bundles and Good Filtered Higgs Bundles. Takuro Mochizuki. SIGMA 17 (2021), 068, 66 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Mochizuki, Takuro
author_facet Mochizuki, Takuro
citation_txt Good Wild Harmonic Bundles and Good Filtered Higgs Bundles. Takuro Mochizuki. SIGMA 17 (2021), 068, 66 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way to construct Frobenius manifolds.
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last_indexed 2026-04-17T18:13:30Z
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spelling Mochizuki, Takuro
2025-12-30T15:54:26Z
2021
Good Wild Harmonic Bundles and Good Filtered Higgs Bundles. Takuro Mochizuki. SIGMA 17 (2021), 068, 66 pages
1815-0659
2020 Mathematics Subject Classification: 53C07; 58E15; 14D21; 81T13
arXiv:1902.08298
https://nasplib.isofts.kiev.ua/handle/123456789/211355
https://doi.org/10.3842/SIGMA.2021.068
We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way to construct Frobenius manifolds.
It is my great pleasure to dedicate this paper to Professor Kyoji Saito on the occasion of his 77th birthday. Not to mention his pioneering and profound achievements, I have always been impressed with his kindness and generosity towards the younger generation of mathematicians, as well as his insatiable quest for mathematics. I appreciate the editors of this special issue for the invitation. I thank Carlos Simpson for his fundamental works on harmonic bundles, which are most important in this study. I am grateful to the referees for their careful readings and helpful comments to improve this manuscript. I thank Philip Boalch and Andy Neitzke for their kind comments on a preliminary note on the proof in the one-dimensional case. I thank Claude Sabbah for discussions on many occasions and for his kindness. I thank Francois Labourie for his comment on the definition of wild harmonic bundles. I thank Pengfei Huang for the discussions. I am grateful to Ya Deng for asking questions related to Mehta-Ramanathan type theorems in Section 3.4 and tensor products in Section 4.3. I thank Akira Ishii and Yoshifumi Tsuchimoto for their constant encouragement. A part of this manuscript was prepared for lectures in the Oka symposium and the ICTS program "Quantum Fields, Geometry and Representation Theory". I thank the organizers for the opportunities. I am partially supported by the Grant-in-Aid for Scienti c Research (S) (No. 17H06127), the Grant-in-Aid for Scienti c Research (S) (No. 16H06335), the Grant-in-Aid for Scienti c Research (A) (No. 21H04429), the Grant-in-Aid for Scienti c Research (C) (No. 15K04843), and the Grant-in-Aid for Scienti c Research (C) (No. 20K03609), Japan Society for the Promotion of Science.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
Article
published earlier
spellingShingle Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
Mochizuki, Takuro
title Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
title_full Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
title_fullStr Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
title_full_unstemmed Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
title_short Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
title_sort good wild harmonic bundles and good filtered higgs bundles
url https://nasplib.isofts.kiev.ua/handle/123456789/211355
work_keys_str_mv AT mochizukitakuro goodwildharmonicbundlesandgoodfilteredhiggsbundles