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Computing $\pi_1$ of the complement of a non-singular plane curve

Another approach is to use Milnor's work on isolated singularities of complex hypersurfaces. More generally, let $W$ be a smooth hypersurface in $\Bbb{CP}^n \,\,(n\geq 2)$ defined by a homogeneous ...
KhashF's user avatar
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4 votes

A formula for the cross-ratio in terms of hyperbolic data

Your formula can be found on page 355 (near the end of Section 7.4) of Marden's book Outer circles: an introduction to hyperbolic 3-manifolds. In the second edition of the book, with the title, ...
Sam Nead's user avatar
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4 votes

Necessary and/or sufficient condition for invertibility of the gradient of a polynomial of $m$ variables, viewed as a self map of $\mathbb{R}^m?$

Condition C is not sufficient. A counterexample is given by $P(x,y)=x^4-2x^2 y^2+y^4=(x^2-y^2)^2$. Then $\nabla P(x,y)=(0,0)$ whenever $x=\pm y$. The OP has now said that the condition (say B) that, ...
Iosif Pinelis's user avatar

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