I recently asked a question regarding tangent cones here: Tangent cone of an arbitrary algebraic curve
After doing some reading, I have another question on how to calculate the delta invariant of these curves. Specifically,I mean the delta invariant referenced here: https://www.maplesoft.com/support/help/maple/view.aspx?path=algcurves%2Fsingularities.
I have read that this has something to do with blowing up the curve, but I do not know how to do this for a given curve. I am trying to learn about the classification of singularities if that is any help.
I have repeated the same curve examples from the other question here to illustrate examples.
1.) $f=xy+x+y+1$
2.) $f=x^3-x^2+y^2$
3.) $f=x^3+x^2+y^2$
4.) $f=2x^4-3x^2y+y^2-2y^3+y^4$
Any thoughts/considerations/references would be wonderful. Specifically I love examples. So a reference where the author does a calculation would be incredibly useful to me.
Thanks so much!