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Let $L$ be algebraic curve.

Can we say that, $L$ is a piecewise ${C^\infty }$ curve?

Under sky
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1 Answers1

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You're thinking of an algebraic curve over the reals?

Then yes, because the singular locus is a subvariety and therefore consists of finitely many points.

Daniel McLaury
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  • I need a good reference for 'properties of algebraic curve'. Please guide me. – Under sky Mar 23 '16 at 21:37
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    Well, if you want to know much more than the basics you'd have to learn some algebraic geometry. William Fulton's book on Algebraic Curves is available from his website if you're interested. – Daniel McLaury Mar 23 '16 at 21:38