Geometry & Topology Volume 18, issue 2 (2014)

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Orbifold points on Teichmüller curves and Jacobians with complex multiplication

Ronen E Mukamel

Geometry & Topology 18 (2014) 779–829

DOI: 10.2140/gt.2014.18.779

Bibliography

1	M F Atiyah, Riemann surfaces and spin structures, Ann. Sci. École Norm. Sup. 4 (1971) 47 MR0286136
2	M Bainbridge, Euler characteristics of Teichmüller curves in genus two, Geom. Topol. 11 (2007) 1887 MR2350471
3	M Bainbridge, M Möller, Deligne–Mumford compactification of the real multiplication locus and Teichmüller curves in genus three arXiv:0911.4677
4	C Birkenhake, H Lange, Complex abelian varieties, Grundl. Math. Wissen. 302, Springer (2004) MR2062673
5	O Bolza, On binary sextics with linear transformations into themselves, Amer. J. Math. 10 (1887) 47 MR1505464
6	I I Bouw, M Möller, Differential equations associated with nonarithmetic Fuchsian groups, J. Lond. Math. Soc. 81 (2010) 65 MR2580454
7	I I Bouw, M Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. 172 (2010) 139 MR2680418
8	J H Bruinier, Hilbert modular forms and their applications, from: "The 1–2–3 of modular forms" (editor K Ranestad), Springer (2008) 105 MR2447162
9	K Calta, Veech surfaces and complete periodicity in genus two, J. Amer. Math. Soc. 17 (2004) 871 MR2083470
10	G van der Geer, Hilbert modular surfaces, Ergeb. Math. Grenzgeb. 16, Springer (1988) MR930101
11	S Kerckhoff, H Masur, J Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. 124 (1986) 293 MR855297
12	B Klinger, A Yafaev, The André–Oort conjecture arXiv:1209.0936
13	M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
14	S Lang, Elliptic functions, Graduate Texts in Mathematics 112, Springer (1987) MR890960
15	P Lochak, On arithmetic curves in the moduli spaces of curves, J. Inst. Math. Jussieu 4 (2005) 443 MR2197065
16	J I Manin, Parabolic points and zeta functions of modular curves, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 19 MR0314846
17	H Masur, S Tabachnikov, Rational billiards and flat structures, from: "Handbook of dynamical systems, Vol. 1A" (editors B Hasselblatt, A Katok), North-Holland (2002) 1015 MR1928530
18	C T McMullen, Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc. 16 (2003) 857 MR1992827
19	C T McMullen, Teichmüller curves in genus two: Discriminant and spin, Math. Ann. 333 (2005) 87 MR2169830
20	C T McMullen, Teichmüller curves in genus two: Torsion divisors and ratios of sines, Invent. Math. 165 (2006) 651 MR2242630
21	C T McMullen, Dynamics of $\mathrm{SL}_2(\mathbb R)$ over moduli space in genus two, Ann. of Math. 165 (2007) 397 MR2299738
22	M Möller, Shimura and Teichmüller curves, J. Mod. Dyn. 5 (2011) 1 MR2787595
23	A Prestel, Die elliptischen Fixpunkte der Hilbertschen Modulgruppen, Math. Ann. 177 (1968) 181 MR0228439
24	G Shimura, On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math. 78 (1963) 149 MR0156001
25	G Shimura, Abelian varieties with complex multiplication and modular functions, Princeton Math. Series 46, Princeton Univ. Press (1998) MR1492449
26	R Silhol, Genus $2$ translation surfaces with an order $4$ automorphism, from: "The geometry of Riemann surfaces and abelian varieties" (editors J M Muñoz Porras, S Popescu, R E Rodríguez), Contemp. Math. 397, Amer. Math. Soc. (2006) 207 MR2218010
27	J H Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics 151, Springer (1994) MR1312368
28	J Tits, Le Monstre (d'après R Griess, B Fischer et al), from: "Seminar Bourbaki, Vol. 1983/84", Astérisque 121-122, Soc. Math. France (1985) 105 MR768956
29	W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 MR1005006
30	A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry, I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 437 MR2261104