plane curve singularity
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scholarly journals Monotonic invariants under blowups

2020 ◽  
Vol 31 (12) ◽  
pp. 2050093
Author(s):  
Zhenjian Wang
Keyword(s):  
General Framework ◽  
Plane Curve ◽  
Curve Singularity ◽  
Numerical Invariant ◽  
Plane Curve Singularity ◽  
New Perspective

We prove that the numerical invariant [Formula: see text] of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the curve is non-singular. This provides a new perspective to understand the question posed by Dimca and Greuel. Moreover, our work can be put in the general framework of discovering monotonic invariants under blowups.

scholarly journals The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link

2018 ◽  
Vol 22 (2) ◽  
pp. 645-691 ◽  
Author(s):  
Alexei Oblomkov ◽  
Jacob Rasmussen ◽  
Vivek Shende
Keyword(s):  
Hilbert Scheme ◽  
Plane Curve ◽  
Curve Singularity ◽  
Plane Curve Singularity

On Cohen–Macaulay modules over the plane curve singularity of type $$\varvec{T_{44}}$$ T 44

2017 ◽  
Vol 108 (6) ◽  
pp. 569-579
Author(s):  
Yuriy A. Drozd ◽  
Oleksii Tovpyha
Keyword(s):  
Plane Curve ◽  
Curve Singularity ◽  
Plane Curve Singularity

scholarly journals A regularization approach for estimating the type of a plane curve singularity

2013 ◽  
Vol 479 ◽  
pp. 99-119 ◽  
Author(s):  
Mădălina Hodorog ◽  
Josef Schicho
Keyword(s):  
Plane Curve ◽  
Curve Singularity ◽  
Plane Curve Singularity

scholarly journals Improving the computation of invariants of plane curve singularities

2013 ◽  
Vol 21 (1) ◽  
pp. 51-57
Author(s):  
Muhammad Ahsan Binyamin
Keyword(s):  
Incidence Matrix ◽  
Plane Curve ◽  
Milnor Number ◽  
Curve Singularity ◽  
Plane Curve Singularity ◽  
Plane Curve Singularities ◽  
Resolution Graph ◽  
Curve Singularities

Abstract In this article we present an algorithm to compute the incidence matrix of the resolution graph, the total multiplicities, the strict multiplicities and the Milnor number of a reduced plane curve singularity and its implemetation in Singular

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