## New answers tagged projective-geometry

7
votes

### 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 ...

4
votes

Accepted

### 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, ...

4
votes

Accepted

### 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, ...

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