In $\mathbb{C}\mathbb{P}^2$ we define coordinate triangle to be the one with sides $\{x_0=0\}, \{x_1=0\}$ and $\{x_2=0\}$. How would you define its interior? What kind of equation should it satisfy?
interior of a triangle in $CP^2$
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algebraic-geometry
projective-geometry
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3What interior? ${}{}{}{}$ – 2012-09-23
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1Do they bound any body in the complex projective plane? Each “line” (topologically a $2$-plane in this $4$-dimensional space) intersects one of the other two in only one point. – 2012-09-23
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3Once you remove one of the lines, you are left with the usual affine plane $\mathbb C^2$; if you next remove the other two, which are the coordinate axes, what you get is connected. In other words, the complement of the three lines $\{x_j=0\}$, $j=0,1,2$, is connected, and it does not have any sensible *interior* to speak of. – 2012-09-23