Related papers: Classification of Incidence Scrolls(I)
The aim of this paper is to obtain a classification of the scrolls in Pn which are defined by a one-dimensional family of lines meeting a certain set of linear spaces in Pn, a first classification for genus 0 and 1 is given in paper [1].…
The aim of this paper is the computation of the degree and genus of all incidence scrolls in Pn. For this, we fix the dimension of a linear space which have a base space of this fixed dimension. In this way, we can obtain all the incidence…
We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve…
We define {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or…
Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let $\L=\mathcal O_{\mathbb P^N}(1)|_X$ denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of $\L$ are…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
This paper describes a framework for a systematic classification of spreadsheet errors. This classification or taxonomy of errors is aimed at facilitating analysis and comprehension of the different types of spreadsheet errors. The taxonomy…
We study and classify linearly normal surfaces in $\mathbf{P}^n$, of degree $d$ and sectional genus $g$, such that $d\geq 2g-1$.
In this paper we study the Hilbert scheme of smooth, linearly normal, special scrolls under suitable assumptions on degree, genus and speciality.
We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in…
In this article we study congruences of lines in $\mathbb{P}^n$, and in particular of order one. After giving general results, we obtain a complete classification in the case of $\mathbb{P}^4$ in which the fundamental surface $F$ is in fact…
A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…
An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f) of G are adjacent whenever (i) v = w, or (ii) e = f , or (iii) vw = e or f. An incidence p-colouring…
Acyclic categories were introduced by Kozlov and can be viewed as generalised posets. Similar to posets, one can define their incidence algebras and a related topological complex. We consider the incidence algebra of either a poset or…
We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…
The paper discusses the classification of surfaces of degree 10 and sectional genus 9 and 10. The surfaces of degree at most 9 are described through classical work dating from the last century up to recent years, while surfaces of degree 10…
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…
Let $X\subset \mathbb P^N$ be a scroll over a $m$-dimensional variety $Y$. We find the locally free sheaves on $X$ governing the osculating behavior of $X$, and, under certain dimension assumptions, we compute the cohomology class and the…
The classification of projective elliptic line scrolls with the description of their singular loci is given. In particular we recover Atiyah Theorem by using classical methods.