Given a formal at meromorphic connection over an excellent scheme field of characteristic zero, in previous paper we established existence good structures and Deligne–Malgrange lattice after suitably blowing up. In this paper, reinterpret re fine these results by introducing some related structures. We consider the turning locus , which is set points one cannot achieve structure without show th...

We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with pg > 0. Let X be a Kähler surface with pg > 0. By the Enriques-Kodaira classification (cf. [BHPV]), its minimal model is a K3 or Abelian surface, a surface of general type or an ...

Abstract Zero-divisor codes are constructed using group rings where their generators zero-divisors. Generally, zero-divisor can be equivalent despite associated groups non-isomorphic, leading to the proposed conjecture “Every dihedral code has an form of cyclic code”. This paper is devoted study equivalence in $$F_2G$$ <mml:ms...

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

Remark 1. We quickly recall a couple of definitions Let DivQ(X) := Div(X)⊗Q. On smooth projective surfaces all Q-Weil divisors are also Q-Cartier, hence we can write Q-Cartier every divisor D as a finite sum ∑ xiCi, where the Ci are distinct integral curves and xi ∈ Q. A divisor D is called effective (or sometimes positive) if xi ≥ 0 ∀i. If D · C ≥ 0 for all integral curves C then D we be calle...