Advanced Search
Article Contents
Article Contents

Weierstrass filtration on Teichmüller curves and Lyapunov exponents

Abstract Related Papers Cited by
  • We define the Weierstrass filtration for Teichmüller curves and construct the Harder-Narasimhan filtration of the Hodge bundle of a Teichmüller curve in hyperelliptic loci and low-genus nonvarying strata. As a result we obtain the sum of Lyapunov exponents of Teichmüller curves in these strata.
    Mathematics Subject Classification: Primary: 32G15; Secondary: 14H10.


    \begin{equation} \\ \end{equation}
  • [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.


    M. Bainbridge, Euler characteristics of Teichmüller curves in genus two, Geom. Topol., 11 (2007), 1887-2073.doi: 10.2140/gt.2007.11.1887.


    E. M. Bullock, "Subcanonical Points on Algebraic Curves,'' Ph.D. Thesis, Harvard University, 2009.


    I. Bouw and M. Möller, Teichmüller cuves, triangle groups, and Lyapunov exponents, Ann of Math. (2), 172 (2010), 139-185.doi: 10.4007/annals.2010.172.139.


    D. Chen, Square-tiled surfaces and rigid curves on moduli spaces, Adv. Math., 228 (2011), 1135-1162.doi: 10.1016/j.aim.2011.06.002.


    D. Chen and M. Möller, Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus, Geom. Topol., 16 (2012), 2427-2479.


    D. Chen and M. MöllerQuadratic differentials in low genus: Exceptional and non-varying, to appear in Ann. Sci. École Norm. Sup.


    A. Eskin, M. Kontsevich and A. Zorich, Lyapunov spectrum of square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 319-353.doi: 10.3934/jmd.2011.5.319.


    A. Eskin, M. Kontsevich and A. ZorichSum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, arXiv:1112.5872.


    A. Eskin, H. Masur and A. Zorich, Moduli spaces of Abelian differentials: The principal boundary, counting problems and the Siegel-Veech constats, Publ. Math. Inst. Hautes Études Sci., 97 (2003), 61-179.doi: 10.1007/s10240-003-0015-1.


    G. Forni, C. Matheus and A. Zorich, Square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 285-318.doi: 10.3934/jmd.2011.5.285.


    R. Hartshorne, "Algebraic Geometry,'' Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977.


    D. Huybrechts and M. Lehn, "The Geometry of Moduli Spaces of Sheaves,'' Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997.


    M. Kontsevich and A. ZorichLyapunov exponents and Hodge theory, arXiv:hep-th/9701164.


    M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math., 153 (2003), 631-678.doi: 10.1007/s00222-003-0303-x.


    E. Lanneau and D.-N. ManhTeichmüller curves generated by Weierstraß Prym eigenforms in genus three, arXiv:1111.2299.


    C. T. McMullen, Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc., 16 (2003), 857-885.doi: 10.1090/S0894-0347-03-00432-6.


    C. T. McMullen, Prym varieties and Teichmüller curves, Duke Math. J., 133 (2006), 569-590.doi: 10.1215/S0012-7094-06-13335-5.


    C. T. McMullen, Foliations of Hilbert modular surfaces, Amer. J. Math., 129 (2007), 183-215.doi: 10.1353/ajm.2007.0002.


    M. Möller, Shimura and Teichmüller curves, J. Mod. Dyn., 5 (2011), 1-32.doi: 10.3934/jmd.2011.5.1.


    M. MöllerPrym covers, theta functions and Kobayashi curves in Hilbert modular surfaces, to appear in Amer. Journal of Math., arXiv:1111.2624.


    M. MöllerTeichmüller curves, mainly from the view point of algebraic geometry, to appear as PCMI Lecture Notes. Available from: http://www.uni-frankfurt.de/fb/fb12/mathematik/ag/personen/moeller/summaries/PCMI.pdf.


    E. Viehweg and K. Zuo, A characterization of Shimura curves in the moduli stack of abelian varieties, J. Diff. Geometry, 66 (2004), 233-287.


    G. Xiao, Fibered algebraic surfaces with low slope, Math. Ann., 276 (1987), 449-466.doi: 10.1007/BF01450841.


    F. Yu and K. ZuoWeierstrass filtration on Teichmüller curves and Lyapunov exponents: Upper bound, arXiv:1209.2733.

  • 加载中

Article Metrics

HTML views() PDF downloads(105) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint