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.
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TL;DR: In this article, the authors developed a cohomological description of various explicit descents in terms of generalized Jacobians, generalizing the known description for hyperelliptic curves, and presented applications of this to the computation of Mordell-Weil groups of Jacobians.
Abstract: We develop a cohomological description of various explicit descents in terms of generalized Jacobians, generalizing the known description for hyperelliptic curves. Specifically, given an integer $n$ dividing the degree of some reduced effective divisor $\mathfrak{m}$ on a curve $C$, we show that multiplication by $n$ on the generalized Jacobian $J_\frak{m}$ factors through an isogeny $\varphi:A_{\mathfrak{m}} \rightarrow J_{\mathfrak{m}}$ whose kernel is naturally the dual of the Galois module $(\operatorname{Pic}(C_{\overline{k}})/\mathfrak{m})[n]$. By geometric class field theory, this corresponds to an abelian covering of $C_{\overline{k}} := C \times_{\operatorname{Spec}{k}} \operatorname{Spec}(\overline{k})$ of exponent $n$ unramified outside $\mathfrak{m}$. The $n$-coverings of $C$ parameterized by explicit descents are the maximal unramified subcoverings of the $k$-forms of this ramified covering. We present applications of this to the computation of Mordell-Weil groups of Jacobians.
4 citations
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TL;DR: In this paper, the authors studied the relationship between local Euler numbers and normalized volumes of log canonical surface singularities and showed that the two invariants differ only by a factor 4 when the log canonical pair is an orbifold cone over a marked Riemann surface.
Abstract: Let S be a smooth projective variety and
$$\Delta $$
a simple normal crossing
$${\mathbb {Q}}$$
-divisor with coefficients in (0, 1]. For any ample
$${\mathbb {Q}}$$
-line bundle L over S, we denote by
$$\mathscr {E}(L)$$
the extension sheaf of the orbifold tangent sheaf
$$T_S(-\log (\Delta ))$$
by the structure sheaf
$$\mathcal {O}_S$$
with the extension class
$$c_1(L)$$
. We prove the following two results: These results generalize Tian’s result where
$$-K_S$$
is ample and
$$\Delta =\emptyset $$
. We give two applications of these results. The first is to study a question by Borbon–Spotti about the relationship between local Euler numbers and normalized volumes of log canonical surface singularities. We prove that the two invariants differ only by a factor 4 when the log canonical pair is an orbifold cone over a marked Riemann surface. In particular we complete the computation of Langer’s local Euler numbers for any line arrangements in
$${\mathbb {C}}^2$$
. The second application is to derive Miyaoka–Yau-type inequalities on K-semistable log-smooth Fano pairs and Calabi–Yau pairs, which generalize some Chern-number inequalities proved by Song–Wang.
4 citations
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TL;DR: In this paper, the authors investigated the injectivity of the maps Cl(A)→Cl((A/fnA)′), where (A/ fnA)') represents the integral closure.
4 citations
01 Jan 2010
TL;DR: In this paper, the structure of POS-groups of order 2m with (2,m) = 1 was studied and a conjecture of Das's was confirmed, which states that a group G is said to be a POS group if for each x in G the cardinality of the set {y ∈ G|o(y )= o(x)} is a divisor of the order of G.
Abstract: A group G is said to be a POS-group if for each x in G the cardinality of the set {y ∈ G|o(y )= o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups of order 2m with (2,m) = 1, and confirm a conjecture of Das’s.
4 citations
•
Rohm1
TL;DR: In this article, a plurality of drive ICs (7) are mounted on a thermal printhead (1) which has a predetermined number of heating dots (3), and the number of output bits of each drive IC is set to be a divisor of 1/4 of the predetermined number and a multiple of 8 which is no less than 48.
Abstract: According to the present invention, a plurality of drive ICs (7) are mounted on a thermal printhead (1) which has a predetermined number of heating dots (3). The number of output bits of each drive IC (7) is set to be a divisor of 1/4 of the predetermined number of the heating dots (3) and a multiple of 8 which is no less than 48. Thus, it is possible to divide the plurality of drive ICs (7) into 2 or 4 groups and to control the groups of drive ICs by time division. Further, when the number of output bits of each drive IC (7) is set to be a common divisor of 1/4 and 1/3 of the predetermined number of the heating dots (3), it is possible to drive the thermal printhead (1) by 3-divisional control in addition to 2- and 4-divisional control. Specifically, the number of output bits of each drive IC (7) is preferably any one of 72, 144 or 216, in particular 144.
4 citations