منابع مشابه
Strata of rational space curves
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...
متن کاملSmall rational curves on the moduli space of stable bundles
For a smooth projective curve C with genus g ≥ 2 and a degree 1 line bundle L on C, let M := SUC(r,L) be the moduli space of stable vector bundles of rank r over C with the fixed determinant L. In this paper, we study the small rational curves on M and estimate the codimension of the locus of the small rational curves. In particular, we determine all small rational curves when r = 3.
متن کاملOn the Normal Bundles of Smooth Rational Space Curves
in this note we consider smooth rational curves C of degree n in threedimensional projective space IP 3 (over a closed field of characteristic 0). To avoid trivial exceptions we shall always assume that n ~ 4 (this does not hold however for certain auxiliary curves we shall consider). Let N = N c be the normal bundle of C in IP 3. Since degel(IP3)=4, and d e g c l ( l P 0 = 2 , we have that d e...
متن کاملSet-theoretic generators of rational space curves
We show how to calculate three low degree set-theoretic generators (i.e., algebraic surfaces) for all rational space curves of low degree (degree ≤ 6) as well as for all higher degree rational space curveswhere at least one element of theirμ-basis has degree 1 from a μ-basis of the parametrization. In addition to having low degree, at least two of these surface generators are always ruled surfa...
متن کاملComputing the Chow Variety of Quadratic Space Curves
The Chow variety, introduced in 1937 by Chow and van der Waerden [4], parameterizes algebraic cycles of any fixed dimension and degree in a projective space, each given by its Chow form. The case of curves in IP goes back to an 1848 paper by Cayley [3]. A fundamental problem, addressed by Green and Morrison [8] as well as Gel’fand, Kapranov and Zelevinsky [6, §4.3], is to describe the equations...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2001
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02809908