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Why is the zero set in $\mathbb{C}\times\mathbb{C}$ of a polynomial $f(x,y)$ in two complex variables always non-discrete (no zero of $f$ is isolated)?

  • 0
    Are you asking for a proof?2011-03-07
  • 3
    Don't you mean the zero set in $\mathbb{C}\times\mathbb{C}$?2011-03-07
  • 0
    consider $f(x,a)$ for a fixed value of $y$. this has $\text{deg}_xf$ zeros. varying $a$ continuously gives curves of zeros (the zeros of $f(x,a)$ depend continuously on $a$).2011-03-07

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