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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 generalize the Mumford's result to the superelliptic case, where instead of dividing by 2, they divide by 1 − ε - ε.
Abstract: In 2016, Yuri Zarhin gave formulas for "dividing a point on a hyperelliptic curve by 2." Given a point $P$ on a hyperelliptic curve $\mathcal{C}$, Zarhin gives the Mumford's representation of every degree $g$ divisor $D$ such that $2(D - g \infty) \sim P - \infty$. The aim of this paper is to generalize Zarhin's result to the superelliptic situation; instead of dividing by 2, we divide by $1 - \zeta$. Even though there is no Mumford's representation for superelliptic curves, we give a formula for functions which cut out $D$.
TL;DR: For homogeneous simply connected Hodge manifolds, it was shown in this paper that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors.
Abstract: For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.
01 Apr 1990
TL;DR: An algorithm for integer division that is based on the periodic nature of reciprocals of odd integers is presented and an approach to implementation using systolic arrays is presented.
Abstract: An algorithm for integer division that is based on the periodic nature of reciprocals of odd integers is presented. The method consists of the determination of the value in one period of the reciprocal of odd divisor d (referred to as the B-sequence), multiplication of the dividend D by this value to produce D', and the division of D' by 2/sup n/-1, where n is the length of the B-sequence. The generation of the B-sequence and division by 2/sup n/-1 are addressed in detail. Proofs of correctness are provided for both processes. The algorithms are suitable for VLSI implementation. An approach to implementation using systolic arrays is presented. >
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TL;DR: In this article, the flex divisor of a primitively polarized K3 surface is defined as the locus of all points for which there exists a pencil whose base locus is the same as the one of the points in the plane.
Abstract: The flex divisor of a primitively polarized K3 surface $(X,L)$ of degree $L^2=2d$ is, generically, the locus of all points $x\in X$ for which there exists a pencil $V\subset |L|$ whose base locus is $\{x\}$. We show that the flex divisor lies in the linear system $|n_dL|$ where $n_d=(2d+1)C(d)^2$ and $C(d)$ is the Catalan number. We also show that there is a well-defined notion of flex divisor over the whole moduli space $F_{2d}$ of polarized K3 surfaces.
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TL;DR: In this article, the authors give a description of the formal neighborhoods of the components of the boundary divisor in the Deligne-Mumford moduli stack of stable curves in terms of the extended clutching construction.
Abstract: We give a description of the formal neighborhoods of the components of the boundary divisor in the Deligne-Mumford moduli stack $\overline{{\mathcal M}}_g$ of stable curves in terms of the extended clutching construction that we define. This construction can be viewed as a formal version of the analytic plumbing construction. The advantage of our formal construction is that we can control the effect of changing formal parameters at the marked points that are being glued. As an application, we prove that the 1st infinitesimal neighborhood of the boundary component $\Delta_{1,g-1}$ is canonically isomorphic to the 1st infinitesimal neighborhood in the normal bundle, near the locus ${\mathcal M}_{1,1}\times {\mathcal M}_{g-1,1}\subset \Delta_{1,g-1}$ corresponding to pairs of smooth curves with marked points. As another application, we show how to study the period map near the boundary components $\Delta_{g_1,g_2}$ in terms of the coordinates coming from our extended clutching construction.