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Dear Folks:

I come across the word "cusp" in two different fields and I think they are related. Could anyone specify their relationship for me?? Many thanks!!

the cusp of an algebraic curve: for example: (0,0) is the cusp of the complex algebraic curve y^{2}=x^{3};

the cusp point of a discrete group of SL(2,R) , where SL(2,R) acts on the upper half plane by linear fractional transformation. This terminology usually appears when we talk about modular forms.

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# The relation between two terminology cusp (group & algebraic curve)

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