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Euler characteristics of Teichmüller curves in genus two

Matt Bainbridge

Geometry & Topology 11 (2007) 1887–2073
Bibliography
1 W Abikoff, Degenerating families of Riemann surfaces, Ann. of Math. $(2)$ 105 (1977) 29 MR0442293
2 L V Ahlfors, The complex analytic structure of the space of closed Riemann surfaces., from: "Analytic functions", Princeton Univ. Press (1960) 45 MR0124486
3 J S Athreya, Quantitative recurrence and large deviations for Teichmuller geodesic flow, Geom. Dedicata 119 (2006) 121 MR2247652
4 W L Baily Jr., Satake's compactification of $V_{n}$, Amer. J. Math. 80 (1958) 348 MR0099451
5 W L Baily Jr., On the moduli of Jacobian varieties, Ann. of Math. $(2)$ 71 (1960) 303 MR0110715
6 W L Baily Jr., On the theory of $\theta $-functions, the moduli of abelian varieties, and the moduli of curves, Ann. of Math. $(2)$ 75 (1962) 342 MR0162799
7 M Bainbridge, Billiards in L-shaped tables with barriers arXiv:0705.3271v1
8 L Bers, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc. 67 (1961) 465 MR0130972
9 L Bers, Holomorphic differentials as functions of moduli, Bull. Amer. Math. Soc. 67 (1961) 206 MR0122989
10 L Bers, Fiber spaces over Teichmüller spaces, Acta. Math. 130 (1973) 89 MR0430318
11 L Bers, On spaces of Riemann surfaces with nodes, Bull. Amer. Math. Soc. 80 (1974) 1219 MR0361165
12 L Bers, Finite-dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. $($N.S.$)$ 5 (1981) 131 MR621883
13 C Birkenhake, H Lange, Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (2004) MR2062673
14 A I Borevich, I R Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press (1966) MR0195803
15 N Bourbaki, Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaces topologiques séparés, Actualités Scientifiques et Industrielles, No. 1343, Hermann (1969) 133 MR0276436
16 I Bouw, M Möller, Teichmüller curves, triangle groups, and Lyapunov exponents arXiv:math.AG/0511738
17 K Calta, Veech surfaces and complete periodicity in genus two, J. Amer. Math. Soc. 17 (2004) 871 MR2083470
18 W Chen, Y Ruan, Orbifold Gromov-Witten theory, from: "Orbifolds in mathematics and physics (Madison, WI, 2001)", Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
19 H Cohen, Sums involving the values at negative integers of $L$-functions of quadratic characters, Math. Ann. 217 (1975) 271 MR0382192
20 P Deligne, D Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. (1969) 75 MR0262240
21 A Eskin, H Masur, Asymptotic formulas on flat surfaces, Ergodic Theory Dynam. Systems 21 (2001) 443 MR1827113
22 A Eskin, H Masur, M Schmoll, Billiards in rectangles with barriers, Duke Math. J. 118 (2003) 427 MR1983037
23 A Eskin, H Masur, A Zorich, Moduli spaces of abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants, Publ. Math. Inst. Hautes Études Sci. (2003) 61 MR2010740
24 A Eskin, A Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001) 59 MR1839286
25 A Eskin, A Okounkov, R Pandharipande, The theta characteristic of a branched covering arXiv:math.AG/0312186
26 H Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962) 331 MR0137127
27 P Griffiths, J Harris, Principles of algebraic geometry, Pure and Applied Mathematics, John Wiley & Sons (1978) MR507725
28 R C Gunning, Lectures on complex analytic varieties: The local parametrization theorem, Mathematical Notes, Princeton University Press (1970) MR0273060
29 R C Gunning, H Rossi, Analytic functions of several complex variables, Prentice-Hall (1965) MR0180696
30 E Gutkin, C Judge, Affine mappings of translation surfaces: geometry and arithmetic, Duke Math. J. 103 (2000) 191 MR1760625
31 J Harris, I Morrison, Moduli of curves, Graduate Texts in Mathematics 187, Springer (1998) MR1631825
32 R Hartshorne, Residues and duality, Lecture Notes in Mathematics 20, Springer (1966) MR0222093
33 R Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer (1977) MR0463157
34 F E P Hirzebruch, Hilbert modular surfaces, Enseignement Math. $(2)$ 19 (1973) 183 MR0393045
35 P Hubert, S Lelièvre, Prime arithmetic Teichmüller discs in $\mathcal H(2)$, Israel J. Math. 151 (2006) 281 MR2214127
36 K Ireland, M Rosen, A classical introduction to modern number theory, Graduate Texts in Mathematics 84, Springer (1990) MR1070716
37 E Kani, The number of curves of genus two with elliptic differentials, J. Reine Angew. Math. 485 (1997) 93 MR1442190
38 E Kani, Hurwitz spaces of genus 2 covers of an elliptic curve, Collect. Math. 54 (2003) 1 MR1962943
39 R Kenyon, J Smillie, Billiards on rational-angled triangles, Comment. Math. Helv. 75 (2000) 65 MR1760496
40 S Kerckhoff, H Masur, J Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. $(2)$ 124 (1986) 293 MR855297
41 F F Knudsen, D Mumford, The projectivity of the moduli space of stable curves. I. Preliminaries on “det” and “Div”, Math. Scand. 39 (1976) 19 MR0437541
42 M Kontsevich, Lyapunov exponents and Hodge theory, from: "The mathematical beauty of physics (Saclay, 1996)", Adv. Ser. Math. Phys. 24, World Sci. Publ., River Edge, NJ (1997) 318 MR1490861
43 M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
44 I Kra, Horocyclic coordinates for Riemann surfaces and moduli spaces. I. Teichmüller and Riemann spaces of Kleinian groups, J. Amer. Math. Soc. 3 (1990) 499 MR1049503
45 H B Laufer, Normal two-dimensional singularities, Annals of Mathematics Studies 71, Princeton University Press (1971) MR0320365
46 S Lelièvre, Siegel–Veech constants in $\mathcal H(2)$, Geom. Topol. 10 (2006) 1157 MR2255494
47 S Lelièvre, E Royer, Orbitwise countings in $\mathcal H(2)$ and quasimodular forms, Int. Math. Res. Not. (2006) 30 MR2233718
48 A Marden, Geometric complex coordinates for Teichmüller space, from: "Mathematical aspects of string theory (San Diego, CA, 1986)", Adv. Ser. Math. Phys. 1, World Sci. Publishing (1987) 341 MR915828
49 H Masur, Interval exchange transformations and measured foliations, Ann. of Math. $(2)$ 115 (1982) 169 MR644018
50 H Masur, The growth rate of trajectories of a quadratic differential, Ergodic Theory Dynam. Systems 10 (1990) 151 MR1053805
51 H Masur, S Tabachnikov, Rational billiards and flat structures, from: "Handbook of dynamical systems, Vol. 1A", North-Holland (2002) 1015 MR1928530
52 C T McMullen, Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc. 16 (2003) 857 MR1992827
53 C T McMullen, Teichmüller geodesics of infinite complexity, Acta Math. 191 (2003) 191 MR2051398
54 C T McMullen, Teichmüller curves in genus two: discriminant and spin, Math. Ann. 333 (2005) 87 MR2169830
55 C T McMullen, Teichmüller curves in genus two: the decagon and beyond, J. Reine Angew. Math. 582 (2005) 173 MR2139715
56 C T McMullen, Teichmüller curves in genus two: torsion divisors and ratios of sines, Invent. Math. 165 (2006) 651 MR2242630
57 C T McMullen, Dynamics of $\mathrm{SL}_2(\mathbb R)$ over moduli space in genus two, Ann. of Math. $(2)$ 165 (2007) 397 MR2299738
58 C T McMullen, Foliations of Hilbert modular surfaces, Amer. J. Math. 129 (2007) 183 MR2288740
59 T Miyake, Modular forms, Springer (1989) MR1021004
60 M Möller, Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve, Invent. Math. 165 (2006) 633 MR2242629
61 D Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. (1961) 5 MR0153682
62 D Mumford, The structure of the moduli spaces of curves and Abelian varieties, from: "Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1", Gauthier-Villars (1971) 457 MR0441983
63 D Mumford, Hirzebruch's proportionality theorem in the noncompact case, Invent. Math. 42 (1977) 239 MR471627
64 D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, Vol. II", Progr. Math. 36, Birkhäuser (1983) 271 MR717614
65 D Mumford, The red book of varieties and schemes, Lecture Notes in Mathematics 1358, Springer (1999) MR1748380
66 Y Namikawa, On the canonical holomorphic map from the moduli space of stable curves to the Igusa monoidal transform, Nagoya Math. J. 52 (1973) 197 MR0337981
67 M Ratner, Invariant measures and orbit closures for unipotent actions on homogeneous spaces, Geom. Funct. Anal. 4 (1994) 236 MR1262705
68 I Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 359 MR0079769
69 I Satake, On the compactification of the Siegel space, J. Indian Math. Soc. $($N.S.$)$ 20 (1956) 259 MR0084842
70 M Schmoll, Spaces of elliptic differentials, from: "Algebraic and topological dynamics", Contemp. Math. 385, Amer. Math. Soc. (2005) 303 MR2180242
71 J P Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, Grenoble 6 (1955–1956) 1 MR0082175
72 J P Serre, Groupes algébriques et corps de classes, Publications de l’institut de mathématique de l’université de Nancago, VII. Hermann, Paris (1959) 202 MR0103191
73 C L Siegel, The volume of the fundamental domain for some infinite groups, Trans. Amer. Math. Soc. 39 (1936) 209 MR1501843
74 C L Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1969 (1969) 87 MR0252349
75 G van der Geer, Hilbert modular surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Springer (1988) MR930101
76 W A Veech, The Teichmüller geodesic flow, Ann. of Math. $(2)$ 124 (1986) 441 MR866707
77 W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 MR1005006
78 W A Veech, Moduli spaces of quadratic differentials, J. Analyse Math. 55 (1990) 117 MR1094714
79 W A Veech, The billiard in a regular polygon, Geom. Funct. Anal. 2 (1992) 341 MR1177316
80 W A Veech, Siegel measures, Ann. of Math. $(2)$ 148 (1998) 895 MR1670061
81 H Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, MA-London-Don Mills, Ont. (1972) MR0387634
82 S A Wolpert, On obtaining a positive line bundle from the Weil-Petersson class, Amer. J. Math. 107 (1985) MR815769
83 O Zariski, P Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Princeton, NJ-Toronto-London-New York (1960) MR0120249
84 A Zorich, How do the leaves of a closed $1$–form wind around a surface?, from: "Pseudoperiodic topology", Amer. Math. Soc. Transl. Ser. 2 197, Amer. Math. Soc. (1999) 135 MR1733872
85 A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry. I", Springer (2006) 437 MR2261104