We show that a rational normal scroll can in general be set-theoretically defined by a proper subset of the 2-minors of the associated two-row matrix. This allows us to find a class of rational normal scrolls that are almost settheoretic complete intersections.

It is proved for each d, 1 ≤ d ≤ n−1, that a primary 0-dimensional scheme in Pn of degree n + 2 + d in linearly general position lies in a rational normal scroll of dimension d.

We show that the arithmetic depth of the projection Xp of a rational normal scroll X̃ ⊂ P K from a point p ∈ P K \X̃ can be expressed in terms of the rank of the matrix M ′(p), where M ′ is the matrix of linear forms whose 3× 3 minors define the secant variety of X̃.

The μ-invariant μ = (μ1, μ2, μ3) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same μ-type, what we call a μ-stratum, and as well the closure of strata. Many of our results are based on papers by the second author that appeared in the commutative algebra literature. We also present new resul...

Let A be the homogeneous coordinate ring of a rational normal scroll. The ring A is equal to the quotient of a polynomial ring S by the ideal generated by the two by two minors of a scroll matrix ψ with two rows and l catalecticant blocks. The class group of A is cyclic, and is infinite provided l is at least two. One generator of the class group is [J], where J is the ideal of A generated by t...

In this thesis we give a complete description of the syzygies of irreducible, nonsingular, canoncial curves C of genus 9. This includes a collection of all possible Betti tables for C. Moreover a direct correspondence between these Betti tables and the number and types of special linear series on C is given. Especially for Cliff(C) = 3 the curve C is contained in determinantal surface Y on a 4d...

Based on thermodynamic and mechanical models. the axial and tangential forces acting on the orbiting scroll and their balance methods are discussed in this paper. Besides, a detailed analysis of orbiting mechanism of three Pins is carried out too. INTRODUCTION The advantageous characteristics of scroll compressor have been pr1>ved in theory and experiment [ 1 ] [ 3 ] in rer.ent years. Remarking...

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windo...