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 C be a curve over an arbitrary fieldK. An elliptic subcover is a finiteK-morphism f : C → E to an elliptic curve E/K such that its base-change fK : CK → EK to the algebraic closure does not factor over a non-trivial isogeny of EK . If f ′ : C → E ′ is another elliptic subcover, then f ′ is said to be equivalent to f if there is an isomorphism φ : E ∼ → E ′ such that f ′ = φ ◦ f . Let E(C) d...

We describe the Chow ring with rational coefficients of M0,1(P , d) as the subring of invariants of a ring B(M0,1(P , d);Q), relative to the action of the group of symmetries Sd. We compute B(M0,1(P , d);Q) by following a sequence of intermediate spaces for M0,1(P , d). Introduction The moduli spaces of stable maps from curves to smooth projective varieties were introduced by M.Kontsevich and Y...

We describe the Chow ring with rational coefficients of M0,1(P , d) as the subring of invariants of a ring B(M0,1(P , d);Q), relative to the action of the group of symmetries Sd. We compute B(M0,1(P , d);Q) by following a sequence of intermediate spaces for M0,1(P , d). Introduction The moduli spaces of stable maps from curves to smooth projective varieties were introduced by M.Kontsevich and Y...

It is known that Plotkin’s reduction theorem is very important for his theory of universal algebraic geometry [1, 2]. It turns out that this theorem can be generalized to arbitrary categories containing two special objects and in this case its proof becomes considerable more simple. This new proof and applications are the subject of the present paper. INTRODUCTION An automorphism φ of a categor...

Our main results are: (1) The complex and Lagrangian points of a non-complex and nonLagrangian 2n-dimensional submanifold F :M →N , immersed with parallel mean curvature and with equal Kähler angles into a Kähler-Einstein manifold (N, J, g) of complex dimension 2n, are zeros of finite order of sin θ and cos θ respectively, where θ is the common J-Kähler angle. (2) If M is a Cayley submanifold o...

The category of differential graded operads is a cofibrantly generated model category and as such inherits simplicial mapping spaces. The vertices of an operad mapping space are just operad morphisms. The 1-simplices represent homotopies between morphisms in the category of operads. The goal of this paper is to determine the homotopy of the operadic mapping spaces MapO0 (En,C) with a cofibrant ...

The projective moduli variety SUC(2) of semistable rank 2 vector bundles with trivial determinant on a smooth projective curve C comes with a natural morphism φ to the linear series |2Θ| where Θ is the theta divisor on the Jacobian of C. Well-known results of Narasimhan and Ramanan say that φ is an isomorphism to P if C has genus 2 [16], and when C is nonhyperelliptic of genus 3 it is an isomor...

— The category of differential graded operads is a cofibrantly generated model category and as such inherits simplicial mapping spaces. The vertices of an operad mapping space are just operad morphisms. The 1-simplices represent homotopies between morphisms in the category of operads. The goal of this paper is to determine the homotopy of the operadic mapping spaces MapO0 (En,C) with a cofibran...