On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

Rank 2 Ample Vector Bundles on Some Smooth Rational Surfaces

Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with _c2 less than seven on Hirzebruch surfaces, and with _c2 less than four on Del Pezzo surfaces.     

Residues in toric varieties

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y.     

On tensor products of -very ample line bundles

In this paper, we show that the tensor product of -very ample and -very ample line bundles on a complete algebraic variety is -very ample.

     

Regular F-Abundant Semigroups

ABSTRACT

The investigation of regular F-abundant semigroups is initiated. In fact, F-abundant semigroups are generalizations of regular cryptogroups in the class of abundant semigroups. After obtaining some properties of such semigroups, the construction theorem of the class of regular F-abundant semigroups is obtained. In addition, we also prove that a regular F-abundant semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid. Our result is an analogue of that of Gomes and Gould on weakly ample semigroups, and also extends an earlier result of O'Carroll on F-inverse semigroups.     

Ample fields as a basis for possibilistic processes

Ample fields play an important role in possibility theory. These fields of subsets of a universe, which are additionally closed under arbitrary unions, act as the natural domains for possibility measures. A set provided with an ample field is then called an ample space. In this paper we generalise Wang's notions of product ample field and product ample space. We make a topological study of ample spaces and their products, and introduce ample subspaces, extensions and one-point extensions of ample spaces. In this way, a first step towards a mathematical theory of possibilistic processes is made.     

Bounded three-dimensional Fano varieties of integer index

The cube of the anticanonical class of a three-dimensional Fano variety with canonical singularities and integer Fano index is effectively bounded. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 445–451, September, 1999.     

Seshadri constants and the spaces of curves with prescribed singularities and positions

We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X.We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p1,...,pr.Namely,we obtain a universal lower bound on the degree of curves for the existence.It is independent of the position of the singular points.     

On the Birationality of the Bicanonical Map of a Surface Section of a Threefold

Let (?, ?) be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface S ∈ |?| is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless h¹(𝒪_?) = 0 and p_g(S) = 3, 4, 5. This article focuses on the remaining cases which are the hardest, settling the problem.     

Autocorrelations in infinite server batch arrival queues

This paper studies an important aspect of queueing theory, autocorrelation properties of system processes. A general infinite server queue with batch arrivals is considered. There areM different types of customers and their arrivals are regulated by a Markov renewal input process. Batch sizes and service times depend on the relevant customer types. With a conditional approach, closed form expressions are obtained for the autocovariance of the continuous time and prearrival system sizes. Some special models are also discussed, giving insights into steady state system behaviour. Autocorrelation functions have a wide range of applications. We highlight one area of application by using autocovariances to derive variances of sample means for a number of special models.This work has been supported by the Natural Sciences and Engineering Council of Canada through Grant A5639 and by the National Natural Science Foundation of China through Grant 19001015.