We prove that the Hodge metric completion of the Teichmüller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kähler-Einstein metric.

We prove that the Leray spectral sequence in rational cohomology for the quotient map Un,d → Un,d/G where Un,d is the affine variety of equations for smooth hypersurfaces of degree d in P(C) and G is the general linear group, degenerates at E2. 2000 Math. Subj. Class. 14D20, 14L35, 14J70.

We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of coefficients.

Let X1, X2 be mixing connected algebraic dynamical systems with the descending chain condition. We show that every equivariant continuous map X1 → X2 is affine (that is, X2 is topologically rigid) if and only if the system X2 has finite topological entropy.

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of affineness of a generalised connection.

Given a convex n-gon P , a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P . For which polygons P does the ratio Area Q/AreaP have the minimal value? The answer is shown to be: for affine-regular polygons. Mathematics Subject Classification (1991): 52-XX.

In this article, we consider the factor complexity of a fixed point of a primitive substitution canonically defined by a β-numeration system. We provide a necessary and sufficient condition on the Rényi expansion of 1 for having an affine factor complexity map C(n), that is, such that C(n) = an+ b for any n ∈ N.

In this paper we propose a novel approach for matching cartographic images over detecting interest points invariant to scale and affine transformations. Our scale and affine invariant detectors are based on the following recent results: Interest points extracted with the SIFT detector which is adapted to affine transformations and give repeatable results (geometrically stable). This provides a ...

Because of the hairy ball theorem, the only closed 2-manifold that supports a lattice in its tangent space is T . But, if singular points (i.e. points whose tangent space is not endowed with 2 distinct coordinate directions) are allowed, then it becomes possible to give the tangent space a lattice. Because the lattice is well defined everywhere around the points, the effect of moving around the...

We prove that the natural map from the center of the affine Sergeev superalgebra to the even center of any cyclotomic Sergeev superalgebra of odd level is surjective, hence that the even center of a cyclotomic Sergeev superalgebra of odd level consists of symmetric functions in the squares of its polynomial generators.