Geometry & Topology Volume 16, issue 4 (2012)

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Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Dawei Chen and Martin Möller

Geometry & Topology 16 (2012) 2427–2479

DOI: 10.2140/gt.2012.16.2427

Bibliography

1	E Arbarello, M Cornalba, The Picard groups of the moduli spaces of curves, Topology 26 (1987) 153 MR895568
2	E Arbarello, M Cornalba, P A Griffiths, J Harris, Geometry of algebraic curves. Vol. I, Grundl. Math. Wissen. 267, Springer (1985) MR770932
3	M Bainbridge, Euler characteristics of Teichmüller curves in genus two, Geom. Topol. 11 (2007) 1887 MR2350471
4	A Beauville, Complex algebraic surfaces, London Mathematical Society Student Texts 34, Cambridge Univ. Press (1996) MR1406314
5	I Bouw, M Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. 172 (2010) 139
6	L Caporaso, Linear series on semistable curves, Int. Math. Res. Not., rnq 188, 49 pages (2010)
7	D Chen, Covers of elliptic curves and the moduli space of stable curves, J. reine angew. Math. 649 (2010) 167
8	D Chen, Square-tiled surfaces and rigid curves on moduli spaces, Adv. Math. 228 (2011) 1135
9	D Chen, M Möller, Quadratic differentials in low genus: exceptional and non-varying strata arXiv:1204.1707
10	M Cornalba, Moduli of curves and theta-characteristics, from: "Lectures on Riemann surfaces (Trieste, 1987)", World Sci. Publ., Teaneck, NJ (1989) 560 MR1082361
11	I Coskun, Degenerations of surface scrolls and the Gromov-Witten invariants of Grassmannians, J. Algebraic Geom. 15 (2006) 223 MR2199064
12	F Cukierman, Families of Weierstrass points, Duke Math. J. 58 (1989) 317 MR1016424
13	V Delecroix, P Hubert, S Leli‘evre, Diffusion in the periodic wind-tree model arXiv:1107.1810
14	D Eisenbud, J Harris, The Kodaira dimension of the moduli space of curves of genus $\geq\nb 23$, Invent. Math. 90 (1987) 359 MR0910206
15	A Eskin, M Kontsevich, A Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow arXiv:1112.5872
16	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. 97 (2003) 61 MR2010740
17	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
18	G Farkas, Koszul divisors on moduli spaces of curves, Amer. J. Math. 131 (2009) 819 MR2530855
19	G Farkas, The birational type of the moduli space of even spin curves, Adv. Math. 223 (2010) 433
20	G Farkas, A Verra, The geometry of the moduli space of odd spin curves arXiv:1004.0278
21	H M Farkas, Unramified double coverings of hyperelliptic surfaces, J. Analyse Math. 30 (1976) 150 MR0437741
22	G Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle, from: "Handbook of dynamical systems. Vol. 1B", Elsevier B. V., Amsterdam (2006) 549 MR2186248
23	G Forni, C Matheus, An example of a Teichmüller disk in genus 4 with degenerate Kontsevich-Zorich spectrum arXiv:0810.0023
24	J Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983) 221 MR0700769
25	J Harris, Families of smooth curves, Duke Math. J. 51 (1984) 409 MR0747873
26	J Harris, I Morrison, Slopes of effective divisors on the moduli space of stable curves, Invent. Math. 99 (1990) 321 MR1031904
27	J Harris, I Morrison, Moduli of Curves, Graduate Texts in Mathematics 187, Springer (1998) MR1631825
28	J Harris, D Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982) 23 MR664324
29	B Hassett, Stable log surfaces and limits of quartic plane curves, Manuscripta Math. 100 (1999) 469 MR1734796
30	K Kodaira, On compact analytic surfaces. II, III, Ann. of Math. 77 $(1963)$, 563–626; ibid. 78 (1963) 1 MR0184257
31	M Kontsevich, Lyapunov exponents and Hodge theory, from: "The mathematical beauty of physics (Saclay, 1996)", Adv. Ser. Math. Phys. 24, World Sci. Publishing (1997) 318 MR1490861
32	M Kontsevich, A Zorich, Lyapunov exponents and Hodge theory arXiv:hep-th/9701164
33	M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
34	A Logan, The Kodaira dimension of moduli spaces of curves with marked points, Amer. J. Math. 125 (2003) 105 MR1953519
35	H Masur, On a class of geodesics in Teichmüller space, Ann. of Math. 102 (1975) 205 MR0385173
36	M Möller, Variations of Hodge structures of a Teichmüller curve, J. Amer. Math. Soc. 19 (2006) 327 MR2188128
37	M Möller, Shimura and Teichmüller curves, J. Mod. Dyn. 5 (2011) 1 MR2787595
38	S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles, II, Math. Proc. Cambridge Philos. Soc. 105 (1989) 79 MR0966142
39	D Mumford, Stability of projective varieties, Enseignement Math. 23 (1977) 39 MR0450272
40	M Reid, Chapters on algebraic surfaces, from: "Complex algebraic geometry (Park City, UT, 1993)", IAS/Park City Math. Ser. 3, Amer. Math. Soc. (1997) 3 MR1442522
41	F Yu, K Zuo, Weierstrass filtration on Teichmüller curves and Lyaponov exponents arXiv:1203.6053
42	A Zorich, Flat surfaces, from: "Frontiers in Number Theory, Physics and Geometry. Volume 1: On random matrices, zeta functions and dynamical systems", Springer (2006) 439