[AF] E. Aldrovandi and G. Falqui, Geometry of Higgs and Toda fields on Riemann surfaces, J. Geom. Phys. 17 (1995), no. 1, 25–48.
[AG] L. A´lvarez-C´onsul and O. Garc´ıa-Prada, Hitchin-Kobayashi correspon- dence, quivers, and vortices, Comm. Math. Phys. 238 (2003), no. 1-2, 1–33.
[Ban] D. Banfield, The geometry of coupled equations in gauge theory, D. Phil. Thesis, University of Oxford, 1996.
[Bap] J. M. Baptista, Moduli spaces of Abelian vortices on K¨ahler manifolds, preprint, arXiv:1211.0012, 2012.
[Bar1] D. Baraglia, Cyclic Higgs bundles and the affine Toda equations, Geom. Dedicata 174 (2015), 25–42.
[Bar2] D. Baraglia, G2 geometry and integrable systems, Ph.D. Thesis, Uni- versity of Oxford, 2009, arXiv:1002.1767.
[Ber] R.J. Berman, Analytic torsion, vortices and positive Ricci curvature, preprint, arXiv:1006.2988, 2010.
[BG] C.P. Boyer and K.Galicki, Sasakian geometry, Oxford Mathematical Monographs. Oxford University Press, Oxford, 2008. xii+613 pp. ISBN: 978-0-19-856495-9.
[BH1] D. Baraglia and P. Hekmati, A foliated Hitchin-Kobayashi correspon- dence, preprint, arXiv:1802.09699, 2018.
[BH2] D. Baraglia and P. Hekmati, Moduli spaces of contact instantons, Adv.Math. 294 (2016), 562–595.
[BK1] I. Biswas and H. Kasuya, Higgs bundles and flat connections over com- pact Sasakian manifolds, Comm. Math. Phys. 385 (2021), no. 1, 267–290.
[BK2] I. Biswas and H. Kasuya, Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles, preprint, arXiv:2110.10644, 2021
[Br1] S.B. Bradlow, Vortices in holomorphic line bundles over closed K¨ahler manifolds, Comm. Math. Phys. 135 (1990), no. 1, 1-17.
[Br2] S.B. Bradlow, Special metrics and stability for holomorphic bundles with global sections, J. Diff. Geom. 33 (1991), no. 1, 169-213.
[BW] J. A. Bryan and R. Wentworth, The multi-monopole equations for K¨ahler surfaces, Turkish J. Math. 20 (1996), no. 1, 119–128.
[Dem] J.-P. Demailly, Analytic methods in algebraic geometry, Surveys of Modern Mathematics, 1. International Press, Somerville, MA; Higher Ed- ucation Press, Beijing, 2012. viii+231 pp. ISBN: 978-1-57146-234-3.
[DL] S. Dai and Q. Li, On cyclic Higgs bundles, Math. Ann. 376 (2020), no.3-4, 1225–1260.
[Doa] A. Doan, Adiabatic limits and Kazdan-Warner equations, Calc. Var.Partial Differential Equations 57 (2018), no. 5, Art. 124, 25 pp.
[Dol] I. Dolgachev, Lectures on invariant theory, London Mathematical So- ciety Lecture Note Series, 296. Cambridge University Press, Cambridge, 2003. xvi+220 pp. ISBN: 0-521-52548-9.
[Ful] W. Fulton, Introduction to toric varieties, Annals of Mathematics Stud- ies, 131. The William H. Roever Lectures in Geometry. Princeton Univer- sity Press, Princeton, NJ, 1993. xii+157 pp. ISBN: 0-691-00049-2.
[GGM] O. Garc´ıa-Prada, P. B. Gothen and I. Mundet i Riera, The Hitchin- Kobayashi correspondence, Higgs pairs and surface group representations, preprint, arXiv:0909.4487, 2009.
[GH] M. A. Guest, N.-K. Ho, Kostant, Steinberg, and the Stokes matrices of the tt∗-Toda equations, Selecta Math. (N.S.) 25 (2019), no. 3, Paper No. 50, 43 pp.
[GL] M. A. Guest and C.-S. Lin, Nonlinear PDE aspects of the tt∗ equations of Cecotti and Vafa, J. Reine Angew. Math. 689 (2014), 1–32.
[Hit1] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc.London Math. Soc. (3) 55 (1987), no. 1, 59–126.
[Hit2] N. J. Hitchin, Lie groups and Teichmu¨ller space, Topology 31 (1992), no. 3, 449–473.
[HW] A. Haydys and T. Walpuski, A compactness theorem for the Seiberg- Witten equation with multiple spinors in dimension three, Geom. Funct. Anal. 25 (2015), no. 6, 1799–1821.
[JT] A. Jaffe and C. H. Taubes, Vortices and monopoles, Progress in Physics,2. Birkh¨auser, Boston, Mass., 1980. v+287 pp. ISBN: 3-7643-3025-2.
[Kin] A. D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), no. 180, 515-530.
[Kir] F. C. Kirwan, Cohomology of quotients in symplectic and algebraic ge- ometry, Mathematical Notes, 31. Princeton University Press, Princeton, NJ, 1984. i+211 pp. ISBN: 0-691-08370-3.
[KLW] Y. Kordyukov, M. Lejmi, and P. Weber, Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4, J. Geom. Phys. 107 (2016), 114–135.
[KN] G. Kempf and L. Ness, The length of vectors in representation spaces, Algebraic geometry (Proc. Summer Meeting, Univ. Copenhagen, Copen- hagen, 1978), pp. 233–243, Lecture Notes in Math., 732, Springer, Berlin, 1979.
[Kon] H. Konno, The geometry of toric hyperk¨ahler varieties, Toric topology, 241–260, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008.
[Kos] B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973–1032.
[KW] J. L. Kazdan and F. W. Warner, Curvature functions for compact 2-manifolds, Ann. of Math. (2) 99 (1974), 14-47.
[LM1] Q. Li and T. Mochizuki, Complete solutions of Toda equa- tions and cyclic Higgs bundles over non-compact surfaces, preprint, arXiv:2010.05401, 2020.
[LM2] Q. Li and T. Mochizuki, Isolated singularities of Toda equations and cyclic Higgs bundles, preprint, arXiv:2010.06129, 2020.
[LT] M. Lu¨bke and A. Teleman, The Kobayashi-Hitchin correspondence, World Scientific Publishing Co., Inc., River Edge, NJ, 1995. x+254 pp. ISBN: 981-02-2168-1.
[Miy1] N. Miyatake, Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space, Geom Dedicata 214, 651–669 (2021).
[Miy2] N. Miyatake, On diagonal pluriharmonic metrics of G-Higgs bundles, preprint, arXiv:2111.07330, 2021.
[Mor] J. W. Morgan, The Seiberg-Witten equations and applications to the topology of smooth four-manifolds, Mathematical Notes, 44. Princeton Uni- versity Press, Princeton, NJ, 1996.
[Mol] P. Molino, Riemannian foliations, Translated from the French by Grant Cairns. With appendices by Cairns, Y. Carri‘ere, E. Ghys, E. Salem and V. Sergiescu. Progress in Mathematics, ´ 73. Birkh¨auser Boston, Inc., Boston, MA, (1988). 339 pp.
[MP] C. Marchioro and M. Pulvirenti, Mathematical theory of incompress- ible nonviscous fluids, Applied Mathematical Sciences, 96. Springer-Verlag, New York, 1994. xii+283 pp.
[Mum] D. Mumford, The red book of varieties and schemes, Second, ex- panded edition. Includes the Michigan lectures (1974) on curves and their Jacobians. With contributions by Enrico Arbarello. Lecture Notes in Math- ematics, 1358. Springer-Verlag, Berlin, 1999. x+306 pp. ISBN: 3-540- 63293-X.
[MFK] D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory, Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Re- sults in Mathematics and Related Areas (2)], 34. Springer-Verlag, Berlin, 1994. xiv+292 pp. ISBN: 3-540-56963-4.
[Mun] I. Mundet i Riera, A Hitchin-Kobayashi correspondence for K¨ahler fibrations, J. Reine Angew. Math. 528 (2000), 41-80.
[Nak] H. Nakajima, Lectures on Hilbert schemes of points on surfaces, Uni- versity Lecture Series, 18. American Mathematical Society, Providence, RI, 1999. xii+132 pp. ISBN: 0-8218-1956-9.
[New] P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 51. Tata Institute of Fundamental Research, Bombay; by the Narosa Publishing House, New Delhi, 1978. vi+183 pp. ISBN: 0-387-08851- 2.
[Ram] A. Ramanathan, Stable principal bundles on a compact Riemann sur- face, Math. Ann. 213 (1975), 129–152.
[Sim1] C.T. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988), no. 4, 867–918.
[Sim2] C. T. Simpson, Katz’s middle convolution algorithm, Pure Appl. Math. Q. 5 (2009), no. 2, Special Issue: In honor of Friedrich Hirzebruch. Part 1, 781–852.
[Tar] G. Tarantello, Analytical, geometrical and topological aspects of a class of mean field equations on surfaces, Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 931–973.
[Tau] C. H. Taubes, Arbitrary N-vortex solutions to the first order Ginzburg- Landau equations, Comm. Math. Phys. 72 (1980), no. 3, 277–292.
[WZ] D. Wu and X. Zhang, Higgs bundles over foliation manifolds, Sci.China Math. 64, 399–420 (2021).