Connected Components of Strata of Quadratic Differentials over Teichmuller Space
نویسنده
چکیده
In this paper, we study connected components of strata of the space of quadratic differentials lying over Tg. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on the number of such components. For strata with sufficiently many zeroes of the same order we can state precisely the number of
منابع مشابه
Quantitative Recurrence and Large Deviations for Teichmuller Geodesic Flow
We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on the moduli space Qg of holomorphic unit-area quadratic differentials on a compact genus g ≥ 2 surface.
متن کاملQuadratic Differentials in Low Genus: Exceptional and Non-varying Strata
We give an algebraic way of distinguishing the components of the exceptional strata of quadratic differentials in genus three and four. The complete list of these strata is (9,−1), (6, 3,−1), (3, 3, 3,−1) in genus three and (12), (9, 3), (6, 6), (6, 3, 3) and (3, 3, 3, 3) in genus four. The upshot of our method is a detailed study regarding the geometry of canonical curves. This result is part ...
متن کاملExponential 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 کاملSpin 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 کاملQuotient Groups of the Fundamental Groups of Certain Strata of the Moduli Space of Quadratic Differentials
In [6], Kontsevich and Zorich conjecture that the fundamental groups of strata of the moduli space of abelian differentials are commensurable with various mapping class groups. In this paper we consider a similar question for strata of quadratic differentials, and in particular we construct a quotient group of the fundamental group for a certain family of strata. We do so by mapping a stratum i...
متن کامل