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.

H-instanton bundles on three-dimensional polarized projective varieties

Abstract: We propose a notion of instanton bundle (called $H$-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor $H$, that naturally generalizes the ones on $\mathbb{P}^3$ and on the flag threefold $F(0,1,2)$. We discuss the cases of Veronese and Fano threefolds. Then we deal with $H$-instanton bundles $\mathcal{E}$ on three-dimensional rational normal scrolls $S(a_0,a_1,a_2)$. We give a monadic description of $H$-instanton bundles and we prove the existence of $\mu$-stable $H$-instanton bundles on $S(a_0,a_1,a_2)$ for any admissible charge $k=c_2(\mathcal{E})H$. Then we deal in more detail with $S(a,a,b)$ and $S(a_0,a_1,a_2)$ with $a_0+a_1>a_2$ and even degree. Finally we describe a nice component of the moduli space of $\mu$-stable bundles whose points represent $H$-instantons.

Frequency divider presettable to fractional divisors

Abstract: Division by fractions is accomplished with a counter (Z) presettable to integers and a digitally adjustable delay line (V) following this counter. The fractional parts (b) of the divisor, which are held in decimal point representation (a+0.b) in a divisor register (R), are applied to a first adder (A1) followed by a buffer memory (S), and the integral parts (a) of this divisor are applied to a second adder (A2). The output of the buffer memory (S) is coupled to the set input (Es) of the delay line (V) and to the second input (E2) of the first adder (A1). Thus, at the input of the delay line (V), the number corresponding to the fractional parts (b) is continuously increased by the fractional parts (b) until the overflow output (Ao) of the first adder (A1) provides a signal which is applied to the least significant digit (LB) of the first input (E1) of the second adder (A2). One unit is thus added to the integral parts (a), and the counter (Z) counts one additional digit for one cycle. For arbitrary fractional divisors, the maximum phase-jitter amplitude is equal to the smallest adjustable time delay and, hence, considerably smaller than the clock period (T') of the signal to be divided (F).

Semi-continuity for total dimension divisors of étale sheaves

Abstract: In this paper, we extend an inequality that compares the pull-back of the total dimension divisor of an etale sheaf and the total dimension divisor of the pull-back of the sheaf due to Saito. Using this formula, we generalize Deligne and Laumon’s lower semi-continuity property for Swan conductors of etale sheaves on relative curves to higher relative dimensions in a geometric situation.

Capacity and deficient divisors

Abstract: i. We consider a complex m-dimensional manifold Q on which a family of divisors is defined, parametrized by a compact complex n-dimensional manifold Y. We will assume that these objects are defined by the following construction. In the direct product Q × Y an (m + n l)-dimensional submanifold W is defined such that the projection p: W + Q is regular, and the projection ~: W ÷ Y is an open mapping. Then to each point g ~ r there corresponds a divisor S~ = p(~-1(g)) on Q, and, at the same time, to each q ~Q there corresponds a smooth divisor Dq = ~(p-~(q)) on Y.

Multi-point codes from the GGS curves

Abstract: This paper is concerned with the construction of algebraic-geometric (AG) codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with some rational places, which enables us to study multi-point AG codes. Along this line, we characterize explicitly the Weierstrass semigroups and pure gaps by an exhaustive computation for the basis of Riemann-Roch spaces from GGS curves. In addition, we determine the floor of a certain type of divisor and investigate the properties of AG codes. Multi-point codes with excellent parameters are found, among which, a presented code with parameters \begin{document}$ [216,190,\geqslant 18] $\end{document} over \begin{document}$ \mathbb{F}_{64} $\end{document} yields a new record.