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RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
CHARACTERISTIC PLANE CURVES
2015/7/14
Characteristic numbers of families of maps of nodal curves to P2 are de ned as
intersection of natural divisor classes. (This de nition agrees with the usual de nition for
families of plane curves.)...
Local invariants on quotient singularities and a genus formula for weighted plane curves
Local invariants quotient singularities genus formula weighted plane curves Algebraic Geometry
2012/6/30
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
Linear systems associated to unicuspidal rational plane curves
Linear systems associated unicuspidal rational plane curves
2012/2/29
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane cur...
Determinantal representation and subschemes of general plane curves
Determinantal representation subschemes of general plane curves
2011/2/21
Let M = (mij ) be an n × n square matrix of integers. For our purposes, we can assume without loss of generality that M is homogeneous and that the entries are non-increasing going leftward and downwa...
On a General Linear Nonlocal Curvature Flow of Convex Plane Curves
General Linear Nonlocal Curvature Flow Convex Plane Curves
2011/1/17
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal cur-vature flow for convex closed plane curves and discuss the short time existence and asymptotic
convergence behavio...
Let $C$ be a smooth (irreducible) curve of degree $d$ in $\mathbb{P}^{2}$. Let $\mathbb{P}^{2} \hookrightarrow \mathbb{P}^{5}$ be the Veronese embedding and let $\mathcal{I}_{C}$ denote the homogeneo...
Relative Node Polynomials for Plane Curves
Enumerative geometry floor diagram Gromov-Witten theory
2010/12/13
We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees.
Contracting Convex Immersed Closed Plane Curves with Slow Speed of Curvature
Convex Immersed Closed Plane Curves Slow Speed of Curvature
2010/12/13
We study the contraction of a convex immersed plane curve with speed 1 k , where ∈ (0, 1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homo...
Evolution of plane curves with a curvature adjusted tangential velocity
curvature driven flow of plane curves curvature adjusted tangential velocity
2010/12/6
We study evolution of closed embedded plane curves with the normal veloc-ity depending on the curvature, the orientation and position of a curve. We propose a new method of tangential redistribution o...
Topology Determination and Isolation for Implicit Plane Curves
Plane curve topology isolating box certied meshing interval analysis
2013/9/9
A method is proposed to generate an isolation for a plane curve, which is a set of boxes covering the curve, having the same topology as the curve, and approximating the curve to any given precision. ...
Hyperbolic mean curvature flow: Evolution of plane curves
hyperbolic mean curvature °ow hyperbolic Monge-Ampμere equa- tion closed plane curve short-time existence
2018/4/20
In this paper we investigate the one-dimensional hyperbolic mean curvature °ow for closed plane curves. More precisely, we consider a family of closed curves F : S1 ￡[0; T) ! R2 which satisˉes the fol...
<正> In a recent paper the present author has established somerepresentations for a plane curve C in the neighbourhood of a singularpoint O characterized by the property that the tangent t(?) of C at O...