Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

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dc.contributor.authorMochizuki, Takuro
dc.date.accessioned2025-12-30T15:54:26Z
dc.date.issued2021
dc.description.abstractWe 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.
dc.description.sponsorshipIt 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.
dc.identifier.citationGood Wild Harmonic Bundles and Good Filtered Higgs Bundles. Takuro Mochizuki. SIGMA 17 (2021), 068, 66 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.068
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 53C07; 58E15; 14D21; 81T13
dc.identifier.otherarXiv:1902.08298
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211355
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleGood Wild Harmonic Bundles and Good Filtered Higgs Bundles
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік