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Yes you are right about the indefinite hessian. Whether (x-y)^2(x+y)^2 should be considered a crunode is an interesting question. If you take a classification of singularities, you find that x^2-y^2 and (x-y)^2(x+y)^2 have different types, the most important type being the simpler case. I'm not at
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I've never heard the term crunode in my life. Is there a relation to node? The picture depicts what most people would call a node, not a crunode. The stuff about the
Hessian contradicts the picture. This article is in serious
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Taking the simplest case I think the defining characteristic is that the determinant of the hessian is negative, that is the quadratic form is hyperbolic. Acnodes have elliptics quadratic forms and cusps have parabolic forms.
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Yes the info about the
Hessian was wrong, somehow it didn't get corrected last time it was pointed out. I think the term is a little dated, but it is well sourced in certain parts of the literature.--
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must be indefinite. There exist crunodes that are local extrema of the locus function (consider
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all clear wherther the more complex case should really be called a curnode or not.
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