Related papers: Base point free theorems--saturation, b-divisors, …
The detailed study of a quantum free particle on a pointed plane is performed. It is shown that there is no problem with a mysterious ``quantum anticentrifugal force" acting on a free particle on a plane discussed in a very recent paper: M.…
This article is based on lecture notes prepared for the August 2006 Cologne Summer School. The first part contains background material and references for beginners. The second (and main) part is a survey of the current status in the theory…
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state,…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We extend Reider's freeness criterion to normal surfaces of characteristic 0. Let Y be a normal surface. Let D be a nef divisor on Y such that K_Y+D is a Cartier divisor. Let x be a point on Y. If x is a base point of |K_Y+D| and…
We study divisors in the blow-up of $\mathbb{P}^n$ at points in general position that are non-special with respect to the notion of linear speciality introduced in [5]. We describe the cohomology groups of their strict transforms via the…
We show how to use Groebner bases for operads to prove various freeness theorems: freeness of certain operads as nonsymmetric operads, freeness of an operad Q as a P-module for an inclusion P into Q, freeness of a suboperad. This gives new…
This paper shows that on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a smooth curve of genus at least two, the base locus of the generalized theta divisor is large provided the rank is…
In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…
On a metric graph we introduce the notion of a free divisor as a replacement for the notion of a base point free complete linear system on a curve. By means of an example we show that the Clifford inequality is the only obstruction for the…
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in…
We show that if $\mathcal{F}$ is an algebraically integrable foliation on a $\mathbb{Q}$-factorial normal projective variety $X$, $ A, B \geq 0$ are $\mathbb{Q}$-divisors on $X$ with $A$ ample such that $(\mathcal{F}, B)$ is foliated dlt…
We give an overview of partial positivity conditions for line bundles, mostly from a cohomological point of view. Although the current work is to a large extent of expository nature, we present some minor improvements over the existing…
From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set…
We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the…
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
The principle of Batyrev and Manin and its variants gives a precise conjectural interpretation for the dominant term for the number of points of bounded height on an algebraic variety for which the opposite of the canonical line bundle is…
Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By…