The set of points obtained by projecting a quadric from a point off the quadric on a hyperplane has many interesting properties. Hirschfeld and Thas [12, 13] provided a characterization of this set, only by means of its intersection pattern with lines. However, their result only holds when the finite field has even order. Here, we extend their result to finite fields of odd order.

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli spac...

Let C1 and C2 be algebraic plane curves in C such that the curves intersect in d1 · d2 points where d1, d2 are the degrees of the curves respectively. Oka and Sakamoto proved that π1(C \ C1 ∪ C2)) ∼= π1(C \ C1)× π1(C \ C2) [1]. In this paper we prove the converse of Oka and Sakamoto’s result for line arrangements. Let A1 and A2 be non-empty arrangements of lines in C such that π1(M(A1 ∪ A2)) ∼=...

Surface/plane intersection problem is a special case of surface/surface intersection, and is an active area of research across many disciplines in computer-aided geometric design. This paper presents, in general the setting of derivational continuities, (i.e. C, C, and C), a surface/plane intersection algorithm for parametric Bézier triangular surface over triangular domain. The present algorit...

Consider a set of lines in the plane. The lines of induce a cell complex, ! " $# , called the arrangement of , whose vertices are the intersection points of the lines, whose edges are the maximal portions of lines containing no vertices and whose two-dimensional cells are the connected components of %'&)('*,+.-0/ 1 . It is assumed that none of the lines is parallel to the 2 -axis. One of the pr...

Curves can be approximated by straight lines linking consecutive intersection points with a lattice. When consecutive points are close together, censoring one of them reduces the computation, speeding automated image processing, for example in reading hand-written mail addresses, in photo identity, and in video telephony. Under randomness assumptions, a rule for selecting the point to be censor...

Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X 0 (N) associated to the Fricke involution wN . In this note we exhibit some relations among the rational points of C. For each g = 3 (resp. the first g = 4) curve C we found that there are one or more lines (resp. planes) in P whose intersection with C consists entirely of rational Heegner points or the cusp point, whe...