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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...
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...