Covers of moduli surfaces

Exceptional Covers of Surfaces

Consider a finite morphism f : X → Y of smooth, projective varieties over a finite field F. Suppose X is the vanishing locus in PN of r forms of degree at most d. We show that there is a constant C depending only on (N, r, d) and deg( f ) such that if |F| > C, then f (F) : X(F) → Y(F) is injective if and only if it is surjective.

Curvature of Innnite Branched Covers; Application to Moduli of Cubic Surfaces

We study branched coverings in several contexts, proving that under suitable circumstances the cover satisses the same upper curvature bounds as the base space. The rst context is of branched covers of an arbitrary CAT() space over an arbitrary complete convex subset. The second context is of a certain sort of branched cover of a Riemannian manifold over a family of mutually orthogonal submanif...

MODULI SPACES OF BRANCHED COVERS OF VEECH SURFACES I: d-SYMMETRIC DIFFERENTIALS

We give a description of asymptotic quadratic growth rates for geodesic segments on covers of Veech surfaces in terms of the modular fiber parameterizing coverings of a fixed Veech surface. To make the paper self contained we derive the necessary asymptotic formulas from the Gutkin-Judge formula. As an application of the method we define and analyze d-symmetric elliptic differentials and their ...

Covers of the Integers with Odd Moduli

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m divisible by none of 3, 5, 7, 11, 13 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2 ± p w...

COVERS OF KLEIN SURFACES by