ﻻ يوجد ملخص باللغة العربية
We present several methods to construct or identify families of free divisors such as those annihilated by many Euler vector fields, including binomial free divisors, or divisors with triangular discriminant matrix. We show how to create families of quasihomogeneous free divisors through the chain rule or by extending them into the tangent bundle. We also discuss whether general divisors can be extended to free ones by adding components and show that adding a normal crossing divisor to a smooth one will not succeed.
Let $M$ be an $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = cap lbrace I colon I text{is an ideal of} R text{and} x in IM rbrace $. $M$ is said to be a content $R$-module if $x in c(x)M $, for all $x in M$. $B$ is c
The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring, self-vanishing of Ext a
We present versal complex analytic families, over a smooth base and of fibre dimension zero, one, or two, where the discriminant constitutes a free divisor. These families include finite flat maps, versal deformations of reduced curve singularities,
The noble-alkali comagnetometer, developed in recent years, has been shown to be a very accurate measuring device of anomalous magnetic-like fields. An ultra-light relic axion-like particle can source an anomalous field that permeates space, allowing
Let I be a homogeneous ideal of a polynomial ring S. We prove that if the initial ideal J of I, w.r.t. a term order on S, is square-free, then the extremal Betti numbers of S/I and of S/J coincide. In particular, depth(S/I)=depth(S/J) and reg(S/I)=reg(S/J).