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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

5 votes
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Zeros of polynomials as a finite union of manifolds

Consider a polynomial in $d$ variables, $p:\mathbb{R}^{d}\rightarrow\mathbb{R}$. Denote by $\mathcal{C}$ its set of zeros, i.e. $$\mathcal{C}=\{x\in\mathbb{R}^{d}\ |\ p(x)=0\}.$$ Q. Is it possible …