Journal of Modern Dynamics (JMD)

Strata of abelian differentials and the Teichmüller dynamics
Pages: 135 - 152, Issue 1, March 2013

doi:10.3934/jmd.2013.7.135      Abstract        References        Full text (221.5K)           Related Articles

Dawei Chen - Department of Mathematics, Boston College, Chestnut Hill, MA 02467, United States (email)

1 E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, "Geometry of Algebraic Curves," Vol. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 267, Springer-Verlag, New York, 1985.       
2 D. Chen, Covers of elliptic curves and the moduli space of stable curves, J. Reine Angew. Math., 649 (2010), 167-205.       
3 D. Chen, Square-tiled surfaces and rigid curves on moduli spaces, Adv. Math., 228 (2011), 1135-1162.       
4 D. Chen and M. Moeller, Non-varying sums of Lyapunov exponents of Abelian differentials in low genus, Geom. Topol., 16 (2012), 2427-2479.
5 D. Chen and M. Moeller, Quadratic differentials in low genus: Exceptional and non-varying strata, arXiv:1204.1707, (2012).
6 D. Chen, M. Moeller and D. Zagier, Siegel-Veech constants and quasimodular forms, in preparation.
7 F. Cukierman, Families of Weierstrass points, Duke Math. J., 58 (1989), 317-346.       
8 S. Diaz, Porteous's formula for maps between coherent sheaves, Michigan Math. J., 52 (2004), 507-514.       
9 A. Eskin, M. Kontsevich and A. Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, preprint, arXiv:1112.5872, (2011).
10 A. Eskin, H. Masur and 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), 61-179.       
11 A. Eskin and M. Mirzakhani, Invariant and stationary measures for the SL$(2,\mathbb R)$ action on Moduli space, arXiv:1302.3320, (2013).
12 G. Farkas and A. Verra, The classification of universal Jacobians over the moduli space of curves, to appear in Comm. Math. Helv., arXiv:1005.5354.
13 U. Hamenstädt, Signatures of surface bundles and Milnor Wood inequalities, arXiv:1206.0263, (2012).
14 J. Harris and I. Morrison, "Moduli of Curves," Graduate Texts in Mathematics, 187, Springer-Verlag, New York, 1998.       
15 J. Harris and D. Mumford, On the Kodaira dimension of the moduli space of curves, With an appendix by William Fulton, Invent. Math., 67 (1982), 23-88.       
16 David Jensen, Rational fibrations of $\overlineM_{5,1}$ and $\overlineM_{6,1}$, J. Pure Appl. Algebra, 216 (2012), 633-642.       
17 David Jensen, Birational contractions of $\overlineM_{3,1}$ and $\overlineM_{4,1}$, Trans. Amer. Math. Soc., 365 (2013), 2863-2879.       
18 A. Kokotov, D. Korotkin and P. Zograf, Isomonodromic tau function on the space of admissible covers, Adv. Math., 227 (2011), 586-600.       
19 M. Kontsevich, Lyapunov exponents and Hodge theory, in "The Mathematical Beauty of Physics" (Saclay, 1996), Adv. Ser. Math. Phys., 24, World Sci. Publishing, River Edge, NJ, (1997), 318-332.       
20 M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math., 153 (2003), 631-678.       
21 D. Korotkin and P. Zograf, Tau function and moduli of differentials, Math. Res. Lett., 18 (2011), 447-458.       
22 R. Lazarsfeld, "Positivity in Algebraic Geometry. I. Classical Setting: Line Bundles and Linear Series," Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas, 3rd Series, A Series of Modern Surveys in Mathematics], 48, Springer-Verlag, Berlin, 2004.       
23 A. Logan, The Kodaira dimension of moduli spaces of curves with marked points, Amer. J. Math., 125 (2003), 105-138.       
24 W. Rulla, "The Birational Geometry of Moduli Space $M(3)$ and Moduli Space $M(2,1)$," Ph.D. Thesis, The University of Texas at Austin, 2001.       
25 B. Thomas, Excess porteous, coherent porteous, and the hyperelliptic locus in $\overline{\mathcal M}_3$, Michigan Math. J., 61 (2012), 359-383.       
26 G. van der Geer and A. Kouvidakis, The Hodge bundle on Hurwitz spaces, Pure Appl. Math. Q., 7 (2011), 1297-1307.       
27 F. Yu and K. Zuo, Weierstrass filtration on Teichmüller curves and Lyapunov exponents, to appear in J. Mod. Dyn., arXiv:1203.6053.
28 A. Zorich, Flat surfaces, in "Frontiers in Number Theory, Physics and Geometry. 1," Springer, Berlin, (2006), 437-583.       
29 D. Zvonkine, personal communication.

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