Geometry & Topology Volume 29, issue 2 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Monodromy of Schwarzian equations with regular singularities

Gianluca Faraco and Subhojoy Gupta

Geometry & Topology 29 (2025) 549–617

DOI: 10.2140/gt.2025.29.549

Bibliography

1	D G L Allegretti, T Bridgeland, The monodromy of meromorphic projective structures, Trans. Amer. Math. Soc. 373 (2020) 6321 MR4155179
2	S Baba, 2π-grafting and complex projective structures with generic holonomy, Geom. Funct. Anal. 27 (2017) 1017 MR3714716
3	M Bainbridge, C Johnson, C Judge, I Park, Haupt’s theorem for strata of abelian differentials, Israel J. Math. 252 (2022) 429 MR4526837
4	S A Ballas, P L Bowers, A Casella, L Ruffoni, Tame and relatively elliptic ℂℙ¹-structures on the thrice-punctured sphere, Algebr. Geom. Topol. 24 (2024) 4589
5	I Biswas, S Dumitrescu, S Gupta, Branched projective structures on a Riemann surface and logarithmic connections, Doc. Math. 24 (2019) 2299 MR4033817
6	G Calsamiglia, B Deroin, S Francaviglia, Branched projective structures with Fuchsian holonomy, Geom. Topol. 18 (2014) 379 MR3159165
7	D Chen, G Faraco, Period realization of meromorphic differentials with prescribed invariants, Forum Math. Sigma 12 (2024)
8	S Chenakkod, G Faraco, S Gupta, Translation surfaces and periods of meromorphic differentials, Proc. Lond. Math. Soc. 124 (2022) 478 MR4413502
9	D Dumas, Complex projective structures, from: "Handbook of Teichmüller theory, II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc. (2009) 455 MR2497780
10	A L Edmonds, Surface symmetry, I, Michigan Math. J. 29 (1982) 171 MR0654478
11	A L Edmonds, R S Kulkarni, R E Stong, Realizability of branched coverings of surfaces, Trans. Amer. Math. Soc. 282 (1984) 773 MR0732119
12	A Eremenko, Co-axial monodromy, Ann. Sc. Norm. Super. Pisa Cl. Sci. 20 (2020) 619 MR4105912
13	G Faraco, Distances on the moduli space of complex projective structures, Expo. Math. 38 (2020) 407 MR4177950
14	V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
15	D Gallo, M Kapovich, A Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. 151 (2000) 625 MR1765706
16	R C Gunning, Special coordinate coverings of Riemann surfaces, Math. Ann. 170 (1967) 67 MR0207978
17	S Gupta, Monodromy groups of ℂP¹-structures on punctured surfaces, J. Topol. 14 (2021) 538 MR4286048
18	S Gupta, M Mj, Monodromy representations of meromorphic projective structures, Proc. Amer. Math. Soc. 148 (2020) 2069 MR4078090
19	S Gupta, M Mj, Meromorphic projective structures, grafting and the monodromy map, Adv. Math. 383 (2021) 107673 MR4232545
20	O Haupt, Ein Satz über die Abelschen Integrale 1. Gattung, Math. Z. 6 (1920) 219 MR1544406
21	D H Husemoller, Ramified coverings of Riemann surfaces, Duke Math. J. 29 (1962) 167 MR0136726
22	E L Ince, Ordinary differential equations, Dover (1944) MR0010757
23	M Kapovich, Periods of abelian differentials and dynamics, from: "Dynamics: topology and numbers" (editors P Moree, A Pohl, L Snoha, T Ward), Contemp. Math. 744, Amer. Math. Soc. (2020) 297 MR4062570
24	T Le Fils, Periods of abelian differentials with prescribed singularities, Int. Math. Res. Not. 2022 (2022) 5601 MR4406117
25	T Le Fils, Holonomy of complex projective structures on surfaces with prescribed branch data, J. Topol. 16 (2023) 430 MR4575871
26	F Luo, Monodromy groups of projective structures on punctured surfaces, Invent. Math. 111 (1993) 541 MR1202134
27	R Mandelbaum, Branched structures and affine and projective bundles on Riemann surfaces, Trans. Amer. Math. Soc. 183 (1973) 37 MR0325958
28	H H Martens, On a theorem of O Haupt characterizing periods of abelian differentials, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985) 377 MR0802499
29	G Mondello, D Panov, Spherical metrics with conical singularities on a 2-sphere : angle constraints, Int. Math. Res. Not. 2016 (2016) 4937 MR3556430
30	G Mondello, D Panov, Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components, Geom. Funct. Anal. 29 (2019) 1110 MR3990195
31	G Nascimento, Monodromies of projective structures on surface of finite-type, Geom. Dedicata 218 (2024) 1 MR4654135
32	P E Newstead, Geometric invariant theory, from: "Moduli spaces and vector bundles" (editors S B Bradlow, L Brambila-Paz, O García-Prada, S Ramanan), Lond. Math. Soc. Lect. Note Ser. 359, Cambridge Univ. Press (2009) 99 MR2537067
33	J Nielsen, Die Struktur periodischer Transformationen von Flächen, Danske Vid. Selsk. Mat.-Fys. Medd. 15 (1937) 1
34	H Poincaré, Sur les groupes des équations linéaires, Acta Math. 4 (1884) 201 MR1554639
35	H P de Saint-Gervais, Uniformization of Riemann surfaces : revisiting a hundred-year-old theorem, Eur. Math. Soc. (2016) MR3494804