منابع مشابه
Relative node polynomials for plane curves
We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees. The degree of the Severi variety of plane curves of degree d and δ nodes is given by a polynomial in d , provided δ is fixed and d is large enough. We extend this result to generalized Severi varieties parametrizing plane curves that, in addition, satisfy tangency conditions of given orders wit...
متن کاملComputing Node Polynomials for Plane Curves
According to the Göttsche conjecture (now a theorem), the degree N of the Severi variety of plane curves of degree d with δ nodes is given by a polynomial in d, provided d is large enough. These “node polynomials” Nδ(d) were determined by Vainsencher and Kleiman–Piene for δ ≤ 6 and δ ≤ 8, respectively. Building on ideas of Fomin and Mikhalkin, we develop an explicit algorithm for computing all ...
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— In this paper, we give a brief survey on the fundamental group of the complement of a plane curve and its Alexander polynomial. We also introduce the notion of θ-Alexander polynomials and discuss their basic properties. Résumé (Un état des lieux sur les polynômes d’Alexander des courbes planes) Dans cet article, nous donnons un bref état des lieux sur le groupe fondamental du complémentaire d...
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In (0.1) X :S × [0, ω) → IR is the position vector of a family of closed convex plane curves, kN is the curvature vector, with k being the curvature and N the inward pointing normal given by N = −(cos θ, sin θ). The weight function γ(θ) = γ(N) is a function of the normal vector to the curve at each point but does not depend on position in the plane. Equation (0.1) has two significant interpreta...
متن کاملRelative motion and pose from arbitrary plane curves
We show how to recover the position and orientation of a pair of known coplanar conics from a single perspective image. We describe and compare a number of methods for determining this relationship. One uses a simple four point back projection model, and the other utilizing transformation invariants. These results can be extended in a number of ways. Firstly, they can be applied to arbitrary pl...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2011
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-011-0337-x