1 Affine Morphisms Definition 1. Let f : X −→ Y be a morphism of schemes. Then we say f is an affine morphism or that X is affine over Y , if there is a nonempty open cover {Vα}α∈Λ of Y by open affine subsets Vα such that for every α, fVα is also affine. If X is empty (in particular if Y is empty) then f is affine. Any morphism of affine schemes is affine. Any isomorphism is affine, and the aff...

We consider the action of a subtorus of the big torus on a toric variety. The aim of the paper is to define a natural notion of a quotient for this setting and to give an explicit algorithm for the construction of this quotient from the combinatorial data corresponding to the pair consisting of the subtorus and the toric variety. Moreover, we study the relations of such quotients with good quot...

We define a morphism based upon a Latin square that generalizes the Thue-Morse morphism. We prove that fixed points of this morphism are overlap-free sequences, generalizing results of Allouche Shallit and Frid.

Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field Fq2 of order q . If the number of Fq2 -rational points of X satisfies the Hasse-Weil upper bound, then X is said to be Fq2 -maximal. For a point P0 ∈ X (Fq2 ), let π be the morphism arising from the linear series D := |(q + 1)P0|, and let N := dim(D). It is known that N ≥ 2 and that π is ind...

Model verification is to check the correctness of the model implementation comparing with a model specification. The specification is modeling and description properties of a real system. The implementation is the ready to simulation model described from model specification. Our proposed frame work is system morphism based approach, which has various levels of morphism depending on system descr...

Definition 1. Let A be a ring. A graded A-algebra is an A-algebra R which is also a graded ring in such a way that if r ∈ Rd then ar ∈ Rd for all a ∈ A. That is, Rd is an A-submodule of R for all d ≥ 0. Equivalently a graded A-algebra is a morphism of graded rings A −→ R where we grade A by setting A0 = A,An = 0 for n > 0. A morphism of graded A-algebras is a morphism of A-algebras which preser...