Enumeration of Rational Plane Curves Tangent to a Smooth Cubic
نویسندگان
چکیده
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
منابع مشابه
An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...
متن کاملEnumeration of N-fold Tangent Hyperplanes to a Surface
For each 1 ≤ n ≤ 6 we present formulas for the number of n−nodal curves in an n−dimensional linear system on a smooth, projective surface. This yields in particular the numbers of rational curves in the system of hyperplane sections of a generic K3−surface imbedded in IP n by a complete system of curves of genus n as well as the number 17,601,000 of rational (singular) plane quintic curves in a...
متن کاملCubic parametric curves of given tangent and curvature
We propose a constructive solution to the problem of finding a cubic parametric curve in a plane if the tangent vectors (derivatives with respect to the parameter) and signed curvatures are given at its end-points but the end-points themselves are unknown. We also show how these curves can be applied to construct blending curves subject to curvature, arc length, inflection and area constraints.
متن کاملCurves in the Complement of a Smooth Plane Cubic Whose Normalizations Are A
For a smooth plane cubic B, we count curves C of degree d such that the normalizations of C\B are isomorphic to A, for d ≤ 7 (for d = 7 under some assumption). We also count plane rational quartic curves intersecting B at only one
متن کاملOn the enumeration of rational plane curves with tangency conditions
We use twisted stable maps to answer the following question. Let E ⊂ P2 be a smooth cubic. How many rational degree d curves pass through a general points of E , have b specified tangencies with E and c unspecified tangencies, and pass through 3d − 1 − a − 2b − c general points of P2? The answer is given as a generalization of Kontsevich’s recursion. We also investigate more general enumerative...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008