We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

It is well-known that any morphism between two p-compact groups will lift, nonuniquely, to an admissible morphism between the maximal tori. We identify here a class of pcompact group morphisms, the p-toric morphisms, which can be perceived as generalized rational isomorphisms, enjoying the stronger property of lifting uniquely to a morphism between the maximal torus normalizers. We investigate ...

We deal with the maximal bifix code construction which is a natural generalization of a group code construction. For a surjective morphism from a free monoidA∗ onto a completely simple semigroup with an adjoined identityM(G; I, J ; )1 and a submonoid S of M(G; I, J ; )1, under certain conditions, the base of a submonoid −1(S) is a maximal bifix code X. We investigate the relationships between t...

In [3], Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The σ-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the σ-sequence has a close connection to the Dragon curve [8]. We prove that the σ-sequence can not be defined b...

With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the multiplication maps in the commutative polynomial ring. The result follows from a more general theorem about the maximal rank property of a minimal almost split mor...

This short, expository note proves existence of the maximal quotient of a variety by free rational curves. 1. Definition of a maximal free rational quotient Definition 1.1. Let V be a Deligne-Mumford stack over a field k, and denote the smooth locus by V sm ⊂ V . A 1-morphism f : Pk → V sm is a free rational curve to V if fTV is generated by global sections and has positive degree. Let S be an ...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

For any smooth Hurwitz curve H n : X Y + Z = 0 over the finite field F p , an explicit description of its Weierstrass points for morphism lines is presented. As a consequence, bounds on number rational are obtained via Stöhr-Voloch Theory. Further, full automorphism group Aut ( ) as well genera all Galois subcovers with ≠ 3 r computed. Finally, question by F. Torres plane nonsingular maximal cu...

Assume that f : X → Y is a surjective generically finite morphism between smooth projective varieties of general type. In general, it is difficult to conclude any birational property of f from the plurigenera ofX and Y . However, Hacon and Pardini in [HP] (Theorem 3) proved the following theorem for varieties of maximal Albanese dimension (i.e. whose Albanese map are generically finite onto the...

In this paper, which is a sequel of [BKLV], we study the convex-geometric properties cone pseudoeffective $n$-cycles in symmetric product $C_d$ smooth curve $C$. We introduce and Abel-Jacobi faces, related to contractibility morphism classical Brill-Noether varieties. investigate when faces are non-trivial, prove that for $d$ sufficiently large (with respect genus $C$) they form maximal chain p...