[1] Barannikov S., Quantum periods. I. Semi-infinite variations of Hodge structures, Int. Math. Res. Not. 2001
(2001), 1243–1264, arXiv:math.AG/0006193.
[2] Biquard O., Fibr´es de Higgs et connexions int´egrables: le cas logarithmique (diviseur lisse), Ann. Sci. Ecole
Norm. Sup. (4) 30 (1997), 41–96.
[3] Biquard O., Boalch P., Wild non-abelian Hodge theory on curves, Compos. Math. 140 (2004), 179–204,
arXiv:math.DG/0111098.
[4] Bogomolov F.A., Holomorphic tensors and vector bundles on projective manifolds, Math. USSR Izv. 13
(1979), 499–555.
[5] Borne N., Fibr´es paraboliques et champ des racines, Int. Math. Res. Not. 2007 (2007), rnm049, 38 pages,
arXiv:math.AG/0604458.
[6] Borne N., Sur les repr´esentations du groupe fondamental d’une vari´et´e priv´ee d’un diviseur a
` croisements
normaux simples, Indiana Univ. Math. J. 58 (2009), 137–180, arXiv:0704.1236.
[7] Cecotti S., Vafa C., Topological–anti-topological fusion, Nuclear Phys. B 367 (1991), 359–461.
[8] Cecotti S., Vafa C., On classification of N = 2 supersymmetric theories, Comm. Math. Phys. 158 (1993),
569–644, arXiv:hep-th/9211097.
[9] Coates T., Iritani H., Tseng H.H., Wall-crossings in toric Gromov–Witten theory. I. Crepant examples,
Geom. Topol. 13 (2009), 2675–2744, arXiv:math.AG/0611550.
[10] Collier B., Wentworth R., Conformal limits and the Bialynicki-Birula stratification of the space of λconnections, Adv. Math. 350 (2019), 1193–1225, arXiv:1808.01622.
[11] Corlette K., Flat G-bundles with canonical metrics, J. Differential Geom. 28 (1988), 361–382.
[12] Cornalba M., Griffiths P., Analytic cycles and vector bundles on non-compact algebraic varieties, Invent.
Math. 28 (1975), 1–106.
[13] Donagi R., Pantev T., Geometric Langlands and non-abelian Hodge theory, in Geometry, Analysis, and
Algebraic Geometry: Forty Years of the Journal of Differential Geometry, Surv. Differ. Geom., Vol. 13, Int.
Press, Somerville, MA, 2009, 85–116.
[14] Donaldson S.K., A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom. 18 (1983),
269–277.
[15] Donaldson S.K., Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector
bundles, Proc. London Math. Soc. 50 (1985), 1–26.
[16] Donaldson S.K., Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987), 231–247.
[17] Donaldson S.K., Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987),
127–131.
[18] Dubrovin B., Geometry and integrability of topological-antitopological fusion, Comm. Math. Phys. 152
(1993), 539–564, arXiv:hep-th/9206037.
[19] Gieseker D., On a theorem of Bogomolov on Chern classes of stable bundles, Amer. J. Math. 101 (1979),
77–85.
A Self-archived copy in
Kyoto University Research Information Repository
https://repository.kulib.kyoto-u.ac.jp
Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
65
[20] Grothendieck A., Techniques de construction et th´eor`emes d’existence en g´eom´etrie alg´ebrique. IV. Les
sch´emas de Hilbert, in S´eminaire Bourbaki, Vol. 6, Soc. Math. France, Paris, 1961, Exp. No. 221, 28 pages.
[21] Hertling C., tt∗ geometry, Frobenius manifolds, their connections, and the construction for singularities,
J. Reine Angew. Math. 555 (2003), 77–161, arXiv:math.AG/0203054.
[22] Hertling C., Sevenheck C., Nilpotent orbits of a generalization of Hodge structures, J. Reine Angew. Math.
609 (2007), 23–80, arXiv:math.AG/0603564.
[23] Hertling C., Sevenheck C., Limits of families of Brieskorn lattices and compactified classifying spaces, Adv.
Math. 223 (2010), 1155–1224, arXiv:0805.4777.
[24] Hitchin N., The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59–126.
[25] Hitchin N., A note on vanishing theorems, in Geometry and Analysis on Manifolds, Progr. Math., Vol. 308,
Birkh¨
auser/Springer, Cham, 2015, 373–382.
[26] Hu Z., Huang P., Simpson–Mochizuki correspondence for λ-flat bundles, arXiv:1905.10765.
[27] Huang P., Non-Abelian Hodge theory and related topics, SIGMA 16 (2020), 029, 34 pages, arXiv:1908.08348.
[28] Iritani H., tt∗ -geometry in quantum cohomology, arXiv:0906.1307.
[29] Iyer J.N.N., Simpson C.T., A relation between the parabolic Chern characters of the de Rham bundles,
Math. Ann. 338 (2007), 347–383, arXiv:math.AG/0603677.
[30] Jost J., Zuo K., Harmonic maps of infinite energy and rigidity results for representations of fundamental
groups of quasiprojective varieties, J. Differential Geom. 47 (1997), 469–503.
[31] Kashiwara M., Semisimple holonomic D-modules, in Topological Field Theory, Primitive Forms and Related
Topics (Kyoto, 1996), Progr. Math., Vol. 160, Birkh¨
auser Boston, Boston, MA, 1998, 267–271.
[32] Kobayashi S., First Chern class and holomorphic tensor fields, Nagoya Math. J. 77 (1980), 5–11.
[33] Kobayashi S., Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982),
158–162.
[34] Kobayashi S., Differential geometry of holomorphic vector bundles, Seminary Note in the University of
Tokyo, Vol. 41, University of Tokyo, Japan, 1982.
[35] Kobayashi S., Differential geometry of complex vector bundles, Publications of the Mathematical Society of
Japan, Vol. 15, Princeton University Press, Princeton, NJ, 1987.
[36] Kotake T., Ochiai T. (Editors), Non-linear problems in geometry, Proceedings of the Sixth International
Taniguchi Symposium, The Taniguchi Foundation, Tohoku University, Japan, 1979.
[37] Li J., Hermitian–Einstein metrics and Chern number inequalities on parabolic stable bundles over K¨
ahler
manifolds, Comm. Anal. Geom. 8 (2000), 445–475.
[38] Li J., Narasimhan M.S., Hermitian–Einstein metrics on parabolic stable bundles, Acta Math. Sin. (Engl.
Ser.) 15 (1999), 93–114.
[39] L¨
ubke M., Chernklassen von Hermite–Einstein–Vektorb¨
undeln, Math. Ann. 260 (1982), 133–141.
[40] L¨
ubke M., Stability of Einstein–Hermitian vector bundles, Manuscripta Math. 42 (1983), 245–257.
[41] L¨
ubke M., Teleman A., The universal Kobayashi–Hitchin correspondence on Hermitian manifolds, Mem.
Amer. Math. Soc. 183 (2006), vi+97 pages, arXiv:math.DG/0402341.
[42] Maruyama M., Yokogawa K., Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), 77–99.
[43] Mehta V.B., Ramanathan A., Semistable sheaves on projective varieties and their restriction to curves,
Math. Ann. 258 (1982), 213–224.
[44] Mehta V.B., Ramanathan A., Restriction of stable sheaves and representations of the fundamental group,
Invent. Math. 77 (1984), 163–172.
[45] Mehta V.B., Seshadri C.S., Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248
(1980), 205–239.
[46] Mochizuki T., Kobayashi–Hitchin correspondence for tame harmonic bundles and an application, Ast´erisque
309 (2006), viii+117 pages.
[47] Mochizuki T., Asymptotic behaviour of tame harmonic bundles and an application to pure twistor Dmodules. I, Mem. Amer. Math. Soc. 185 (2007), xii+324 pages.
[48] Mochizuki T., Asymptotic behaviour of tame harmonic bundles and an application to pure twistor Dmodules. II, Mem. Amer. Math. Soc. 185 (2007), xii+565 pages.
A Self-archived copy in
Kyoto University Research Information Repository
https://repository.kulib.kyoto-u.ac.jp
66
T. Mochizuki
[49] Mochizuki T., Kobayashi–Hitchin correspondence for tame harmonic bundles. II, Geom. Topol. 13 (2009),
359–455, arXiv:math.DG/0602266.
[50] Mochizuki T., Asymptotic behavior of variation of pure polarized TERP structure, Publ. Res. Inst. Math.
Sci. 47 (2011), 419–534, arXiv:0811.1384.
[51] Mochizuki T., Wild harmonic bundles and wild pure twistor D-modules, Ast´erisque 340 (2011), x+607.
[52] Mochizuki T., Harmonic bundles and Toda lattices with opposite sign I, RIMS Kˆ
okyˆ
uroku Bessatsu, to
appear, arXiv:1301.1718.
[53] Mochizuki T., Harmonic bundles and Toda lattices with opposite sign II, Comm. Math. Phys. 328 (2014),
1159–1198, arXiv:1301.1718.
[54] Mochizuki T., Wild harmonic bundles and twistor D-modules, in Proceedings of the International Congress
of Mathematicians – Seoul 2014, Vol. 1, Kyung Moon Sa, Seoul, 2014, 499–527.
[55] Mochizuki T., Mixed twistor D-modules, Lecture Notes in Math., Vol. 2125, Springer, Cham, 2015.
[56] Mumford D., Projective invariants of projective structures and applications, in Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm, 1963, 526–530.
[57] Mumford D., Lectures on curves on an algebraic surface, Annals of Mathematics Studies, Vol. 59, Princeton
University Press, Princeton, N.J., 1966.
[58] Narasimhan M.S., Seshadri C.S., Stable and unitary vector bundles on a compact Riemann surface, Ann.
of Math. 82 (1965), 540–567.
[59] Sabbah C., Harmonic metrics and connections with irregular singularities, Ann. Inst. Fourier (Grenoble)
49 (1999), 1265–1291, arXiv:math.AG/9905039.
[60] Sabbah C., Polarizable twistor D-modules, Ast´erisque 300 (2005), vi+208 pages, arXiv:math.AG/0503038.
[61] Saito K., Takahashi A., From primitive forms to Frobenius manifolds, in From Hodge Theory to Integrability
and TQFT tt∗ -Geometry, Proc. Sympos. Pure Math., Vol. 78, Amer. Math. Soc., Providence, RI, 2008, 31–
48.
[62] Simpson C.T., Constructing variations of Hodge structure using Yang–Mills theory and applications to
uniformization, J. Amer. Math. Soc. 1 (1988), 867–918.
[63] Simpson C.T., Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), 713–770.
[64] Simpson C.T., Higgs bundles and local systems, Inst. Hautes Etudes
Sci. Publ. Math. 75 (1992), 5–95.
[65] Simpson C.T., The Hodge filtration on nonabelian cohomology, in Algebraic Geometry – Santa Cruz
1995, Proc. Sympos. Pure Math., Vol. 62, Amer. Math. Soc., Providence, RI, 1997, 217–281, arXiv:alggeom/9604005.
[66] Simpson C.T., Mixed twistor structures, arXiv:alg-geom/9705006.
[67] Simpson C.T., Iterated destabilizing modifications for vector bundles with connection, in Vector Bundles
and Complex Geometry, Contemp. Math., Vol. 522, Amer. Math. Soc., Providence, RI, 2010, 183–206,
arXiv:0812.3472.
[68] Siu Y.T., Techniques of extension of analytic objects, Lecture Notes in Pure and Applied Mathematics,
Vol. 8, Marcel Dekker, Inc., New York, 1974.
[69] Siu Y.T., The complex-analyticity of harmonic maps and the strong rigidity of compact K¨
ahler manifolds,
Ann. of Math. 112 (1980), 73–111.
[70] Steer B., Wren A., The Donaldson–Hitchin–Kobayashi correspondence for parabolic bundles over orbifold
surfaces, Canad. J. Math. 53 (2001), 1309–1339.
[71] Takemoto F., Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47 (1972), 29–48.
[72] Takemoto F., Stable vector bundles on algebraic surfaces. II, Nagoya Math. J. 52 (1973), 173–195.
[73] Uhlenbeck K., Yau S.-T., On the existence of Hermitian–Yang–Mills connections in stable vector bundles,
Comm. Pure Appl. Math. 39 (1986), S257–S293.
[74] Uhlenbeck K.K., Connections with Lp bounds on curvature, Comm. Math. Phys. 83 (1982), 31–42.
...