Connected components of strata of Abelian differentials over Teichmüller space

Connected Components of Strata of Quadratic Differentials over Teichmuller Space

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 sam...

Strata of Abelian Differentials and the Teichmüller Dynamics

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 spac...

Dynamics over Teichmüller Space

Newton Polygon Strata in the Moduli Space of Abelian Varieties

Tautological Ring of Strata of Differentials

Strata of k-differentials on smooth curves parameterize sections of the k-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the κ and ψ classes of moduli spaces of pointed smooth curves along with the class η = O(−1) of the Hodge bundle. We show that if there is no pole of order k, then the tautological rin...