Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this article, the vanishing of Bockstein cohomology modules was shown to imply vanishing of certain natural conditions on the Gaussians of the extended Rees ring of the Cohen-Macaulay local ring.
Abstract: Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d$ and let $I$ be an $\mathfrak{m}$-primary ideal Let $G$ be the associated graded ring of $A$ \wrt \ $I$ and let $\R = A[It,t^{-1}]$ be the extended Rees ring of $A$ with respect to $I$ Notice $t^{-1}$ is a non-zero divisor on $\R$ and $\R/t^{-1}\R = G$ So we have \textit{Bockstein operators} $\beta^i \colon H^i_{G_+}(G)(-1) \rt H^{i+1}_{G_+}(G)$ for $i \geq 0$ Since $\beta^{i+1}(+1)\circ \beta^i = 0$ we have \textit{Bockstein cohomology} modules $BH^i(G)$ for $i = 0,\ldots,d$ In this paper we show that certain natural conditions on $I$ implies vanishing of some Bockstein cohomology modules
1 citations
TL;DR: In this article, it was shown that if n! ∈ {3, 5}, then d(n!) is a divisor of n!, and that the only positive integers n such that d(Fn) divides Fn, where Fn is the nth Fibonacci number, are n ∈ [1, 2, 3, 6, 24, 48].
Abstract: Let d(m) be the number of divisors of the positive integer m. Here, we show that if n !∈ {3, 5}, then d(n!) is a divisor of n!. We also show that the only positive integers n such that d(Fn) divides Fn, where Fn is the nth Fibonacci number, are n ∈ {1, 2, 3, 6, 24, 48}.
1 citations
TL;DR: In this article, a disjoint union of a lines and c double lines is considered and the maximal rank of the union is obtained for each pair of lines and double lines.
Abstract: A double line \({C \subset \mathbb{P}^3}\) is a connected divisor of type (2, 0) on a smooth quadric surface. Fix \({(a, c) \in \mathbb{N}^2\ \backslash\ \{(0, 0)\}}\). Let \({X \subset \mathbb{P}^3}\) be a general disjoint union of a lines and c double lines. Then X has maximal rank, i.e. for each \({t \in \mathbb{Z}}\) either \({h^1(\mathcal{I}_X(t)) = 0}\) or \({h^0(\mathcal{I}_X(t)) = 0}\).
1 citations
01 Jan 1976
TL;DR: In this article, the behavior of these and other arithmetical functions f(n) for large values of n has been investigated, and various identities satisfied by these functions have been discussed.
Abstract: The last chapter discussed various identities satisfied by arithmetical functions such as µ(n), ϕ(n), Λ(n), and the divisor functions σ a (n). We now inquire about the behavior of these and other arithmetical functions f(n) for large values of n.
1 citations
Posted Content•
TL;DR: In this article, the authors prove that Stein's holomorphic tangent bundle is holomorphically trivialisable and give a necessary and sufficient condition for its holomorphic tangent bundles to be trivialisable.
Abstract: Let $S$ be an intermediate Kato surface, $D$ the divisor consisting of all rational curves of $S$, $\widetilde{S}$ the universal covering of $S$ and $\widetilde{D}$ the preimage of $D$ in $\widetilde{S}$. We prove two results about the surface $\widetilde{S}\setminus \widetilde{D}$: it is Stein (which was already known when $S$ is either a Enoki or a Inoue-Hirzebruch surface) and we give a necessary and sufficient condition so that its holomorphic tangent bundle is holomorphically trivialisable. ----- Soient $S$ une surface de Kato interm\'ediaire, $D$ le diviseur form\'e des courbes rationnelles de $S$, $\widetilde{S}$ le rev\^etement universel de $S$ et $\widetilde{D}$ la pr\'eimage de $D$ dans $\widetilde{S}$. On donne deux r\'esultats concernant la surface $\widetilde{S}\setminus \widetilde{D}$, \`a savoir qu'elle est de Stein (ce qui \'etait connu dans le cas o\`u $S$ est une surface d'Enoki ou d'Inoue-Hirzebruch) et on donne une condition n\'ecessaire et suffisante pour que son fibr\'e tangent holomorphe soit holomorphiquement trivialisable.
1 citations