Strata of Abelian Differentials and the Teichmüller Dynamics

نویسنده

  • DAWEI CHEN
چکیده

This paper focuses on the interplay between the intersection theory and the Teichmüller dynamics on the moduli space of curves. As applications, we study the cycle class of strata of the Hodge bundle, present an algebraic method to calculate the class of the divisor parameterizing abelian differentials with a non-simple zero, and verify a number of extremal effective divisors on the moduli space of pointed curves in low genus.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spin and Hyperelliptic Structures of Log Twisted Differentials

Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected components, due to spin and hyperelliptic structures. We prove that the spin p...

متن کامل

Decay of Correlations for the Rauzy-veech-zorich Induction Map on the Space of Interval Exchange Transformations and the Central Limit Theorem for the Teichmüller Flow on the Moduli Space of Abelian Differentials

The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 4). A corollary is the Central Limit Theorem for the Teichmüller flow on the moduli space of abelian differentials with prescribed singularities (Theorem 10). The proof of Theorem 4 proceeds by the metho...

متن کامل

Exponential Mixing for the Teichmüller Flow in the Space of Quadratic Differentials

We consider the Teichmüller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for the restriction of the Teichmüller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of...

متن کامل

Non-varying Sums of Lyapunov Exponents of Abelian Differentials in Low Genus

We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.

متن کامل

A Large Deviations Bound for the Teichmüller Flow

Largedeviation rates areobtained for suspension flows over symbolic dynamical systems with a countable alphabet. The method is that of [1]. A corollary of the main results is a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, which extends earlier work of J. Athreya [2]. The “entropy approach” we use is similar to that of [20] (see also [10], [13]).

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013