Milnor's $$\bar \mu $$ -invariant and 2-height of reducible plane curves

1986 ◽  
Vol 46 (5) ◽  
pp. 466-472
Author(s):  
Kunio Murasugi
Keyword(s):  
Plane Curves ◽  
Reducible Plane

On log canonical thresholds of reducible plane curves

1999 ◽  
Vol 121 (4) ◽  
pp. 701-721 ◽  
Author(s):  
Takayasu Kuwata
Keyword(s):  
Plane Curves ◽  
Log Canonical ◽  
Reducible Plane

scholarly journals The secant line variety to the varieties of reducible plane curves

2014 ◽  
Vol 195 (2) ◽  
pp. 423-443 ◽  
Author(s):  
Maria Virginia Catalisano ◽  
Anthony V. Geramita ◽  
Alessandro Gimigliano ◽  
Yong-Su Shin
Keyword(s):  
Plane Curves ◽  
Secant Line ◽  
Reducible Plane

The monodromy of reducible plane curves

1977 ◽  
Vol 40 (2) ◽  
pp. 107-141 ◽  
Author(s):  
D. W. Sumners ◽  
J. M. Woods
Keyword(s):  
Plane Curves ◽  
Reducible Plane

scholarly journals Classification of Reducible Plane Curves

1988 ◽  
Vol 11 (2) ◽  
pp. 363-379 ◽  
Author(s):  
Shigeru IITAKA
Keyword(s):  
Plane Curves ◽  
Reducible Plane

scholarly journals On a method of dealing with the intersections of plane curves

1904 ◽  
Vol 5 (4) ◽  
pp. 385-385 ◽  
Author(s):  
F. S. Macaulay
Keyword(s):  
Plane Curves

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane
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