Semi-stable holomorphic vector bundles over generalized Kähler manifolds

References

• Goto R. Moduli spaces of Einstein–Hermitian generalized connections over generalized Kähler manifolds of symplectic type. 2017; arXiv:1707.03143.
   Google Scholar
• Goto R. Kobayashi–Hitchin correspondence of generalized holomorphic vector bundles over generalized Kähler manifolds of symplectic type. 2019; arXiv:1903.07425.
   Google Scholar
• Narasimhan MS, Seshadri CS. Stable and unitary vector bundles on a compact Riemann surface. Ann Math. 1965;82(2):540–567.
   Web of Science ®Google Scholar
• Donaldson SK. Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles. Proc London Math Soc. 1985;3(1):1–26.
   Google Scholar
• Uhlenbeck KK, Yau ST. On the existence of Hermitian–Yang–Mills connections in stable vector bundles. Commun Pure Appl Math. 1986;39(S1):S257–S293.
   Web of Science ®Google Scholar
• Buchdahl NP. Hermitian–Einstein connections and stable vector bundles over compact complex surfaces. Math Ann. 1988;280(4):625–648.
   Web of Science ®Google Scholar
• Li J, Yau ST. Hermitian–Yang–Mills connection on non-Kähler manifolds. In Mathematical aspects of string theory. New York: World Scientific; 1987. p. 560–573.
   Google Scholar
• Álvarez-Cónsul L, García-Prada O. Hitchin–Kobayashi correspondence, quivers, and vortices. Commun Math Phys. 2003;238(1-2):1–33.
   Web of Science ®Google Scholar
• Baraglia D, Hekmati P. A foliated Hitchin-Kobayashi correspondence. 2018; arXiv:1802.09699.
   Google Scholar
• Biswas I, Loftin J, Stemmler M. The vortex equation on affine manifolds. Trans Am Math Soc. 2014;366(7):3925–3941.
   Web of Science ®Google Scholar
• Bradlow SB. Special metrics and stability for holomorphic bundles with global sections. J Differ Geom. 1991;33:169–213.
   Web of Science ®Google Scholar
• Buchdahl NP, Schumacher G. Polystability and the Hitchin-Kobayashi correspondence. 2020; arXiv:2002.03548.
   Google Scholar
• Hitchin NJ. The self-duality equations on a Riemann surface. Proc Lond Math Soc. 1987;3(1):59–126.
   Google Scholar
• Hu Z, Huang P. The Hitchin–Kobayashi correspondence for quiver bundles over generalized Kähler manifolds. J Geom Anal. 2020;30(4):3641–3671.
   Web of Science ®Google Scholar
• Hu S, Moraru R, Seyyedali R. A Kobayashi–Hitchin correspondence for I±-holomorphic bundles. Adv Math. 2016;287:519–566.
   Web of Science ®Google Scholar
• Li J, Zhang C, Zhang X. Semi-stable Higgs sheaves and Bogomolov type inequality. Calc Var Partial Differ Equ. 2017;56(3):159.
   Web of Science ®Google Scholar
• Mochizuki T. Kobayashi–Hitchin correspondence for analytically stable bundles. Trans Am Math Soc. 2020;373(1):551–596.
   Web of Science ®Google Scholar
• Mundet i Riera I. A Hitchin–Kobayashi correspondence for Kähler fibrations. J Reine Angew Math. 2000;528:41–80.
   Web of Science ®Google Scholar
• Pan C, Zhang C, Zhang X. Semi-stable higgs bundles and flat bundles over non-Kähler manifolds. 2019; arXiv:1911.03593.
   Google Scholar
• Simpson CT. Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization. J Am Math Soc. 1988;1(4):867–867.
   Google Scholar
• Shen Z, Zhang C, Zhang X. Flat Higgs bundles over non-compact affine Gauduchon manifolds. 2019; arXiv:1909.12577.
   Google Scholar
• Shen Z, Zhang P. Canonical metrics on holomorphic filtrations over compact Hermitian manifolds. Commun Math Stat. 2020;8:219–237.
   Web of Science ®Google Scholar
• Venugopalan S. Yang–Mills heat flow on gauged holomorphic maps. J Symplect Geom. 2016;14(3):903–981.
   Web of Science ®Google Scholar
• Wu D, Zhang X. Higgs bundles over foliation manifolds. Sci China Math. 2020. https://doi.org/https://doi.org/10.1007/s11425-019-1736-4.
   Google Scholar
• Yoshino M. A Kobayashi-Hitchin correspondence between Dirac-type singular mini-holomorphic bundles and HE-monopoles. 2019; arXiv:1902.09995.
   Google Scholar
• Kobayashi S. Differential geometry of complex vector bundles. Princeton (NJ): Princeton University Press; 1987. (Publications of the Mathematical Society of Japan; 15).
   Google Scholar
• Bruzzo U, Otero BG. Metrics on semistable and numerically effective Higgs bundles. J Reine Angew Math. 2007;612:59–79.
   Web of Science ®Google Scholar
• Cardona SAH. Approximate Hermitian–Yang–Mills structures and semistability for Higgs bundles, I: generalities and the one-dimensional case. Ann Global Anal Geom. 2012;42(3):349–370.
   Web of Science ®Google Scholar
• Jacob A. Existence of approximate Hermitian–Einstein structures on semi-stable bundles. Asian J Math. 2014;18(5):859–884.
   Web of Science ®Google Scholar
• Li J, Zhang X. Existence of approximate Hermitian–Einstein structures on semi-stable Higgs bundles. Calc Var Partial Differ Equ. 2015;52(3-4):783–795.
   Web of Science ®Google Scholar
• Nie Y, Zhang X. Semistable Higgs bundles over compact Gauduchon manifolds. J Geom Anal. 2018;28(1):627–642.
   Web of Science ®Google Scholar
• Zhang C, Zhang P, Zhang X. Higgs bundles over non-compact Gauduchon manifolds. Trans Am Math Soc. 2020. https://doi.org/https://doi.org/10.1090/tran/8323.
   Google Scholar
• Lübke M, Teleman A. The Kobayashi–Hitchin correspondence. Beijing: World Scientific Publishing; 1995.
   Google Scholar
• Kobayashi S. Curvature and stability of vector bundles. Proc Jpn Acad Ser A: Math Sci. 1982;58(4):158–162.
   Google Scholar
• Gualtieri M. Generalized complex geometry. Ann Math. 2011;174(1):75–123.
   Web of Science ®Google Scholar
• Zhang P. Canonical metrics on holomorphic bundles over compact bi-Hermitian manifolds. J Geom Phys. 2019;144:15–27.
   Web of Science ®Google Scholar
• Hitchin NJ. Generalized holomorphic bundles and the B-field action. J Geom Phys. 2011;61(1):352–362.
   Web of Science ®Google Scholar
• Lübke M. Stability of Einstein–Hermitian vector bundles. Manuscr Math. 1983;42(2-3):245–257.
   Web of Science ®Google Scholar