Essential surfaces and tameness of covers.

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.

COVERS OF KLEIN SURFACES by

Essential positive covers of the cube

Linial and Radhakrishnan introduced the following problem. A pair (a, c) with a ∈ R and c ∈ R defines the hyperplane {x : ∑ i aixi = c} ⊂ R. Say that a collection of hyperplanes (a, c), . . . , (a, c) is an essential cover of the cube {0, 1} if it is a cover, with no redundant hyperplanes, and every co-ordinate used: i.e., every point in {0, 1} is contained in some hyperplane; for every j ∈ [m]...

Tameness and Extending Frames

We combine two notions in AECs, tameness and good λ-frames, and show that they together give a very well-behaved nonforking notion in all cardinalities. This helps to fill a longstanding gap in classification theory of tame AECs and increases the applicability of frames. Along the way, we prove a complete stability transfer theorem and uniqueness of limit models in these AECs.

Teichmüller Polynomials, Alexander Polynomials and Finite Covers of Surfaces

In this article we explore a connection between finite covers of surfaces and the Teichmüller polynomial of a fibered face of a hyperbolic 3–manifold. We consider the action of a homological pseudo-Anosov homeomorphism ψ on the homology groups of a class of finite abelian covers of a surface Σg,n. Eigenspaces of the deck group actions on these covers are naturally parametrized by rational point...