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Add example and add figure for it, some small fixes
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jirilebl committed Dec 8, 2023
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Expand Up @@ -174,9 +174,11 @@ and that's more consistent.
renumbered.
<li> Simplify the statement in 6.5.4.
<li> Define the dimension of a subvariety and the concept of pure dimension
using only regular points, that way we get around the technicality
that we never prove that the set of regular points is dense in general.
using only regular points, which seems a little ontologically simpler.
Also simplifies the last exercise in 6.5.
<li> Add the intersection of two complex manifolds to example 6.5.6,
and add the relevant figure.
Also rename X and Y to U and M so that the naming in the example makes more sense.
<li> Move the statement of the theorem about \(Z_f\) to section 6.5 from
6.6 (now Theorem 6.5.9), and add the generalization of this result (that
regular points exist and are thus dense) to arbitrary varieties,
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234 changes: 234 additions & 0 deletions figures/intersect.eepic
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\pgftext[at={\pgfpoint{-0.055348in}{0.75in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}\footnotesize $0$}}}
\pgftext[at={\pgfpoint{-0.055348in}{1.5in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}\footnotesize $1$}}}
\pgfsetlinewidth{0.8pt}
\draw (0in,0in)--(2.25in,1.5in);
\draw (0in,1.5in)--(2.25in,0in);
\end{tikzpicture}
49 changes: 49 additions & 0 deletions figures/intersect.xp
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/* slightly modified sample from epix samples gallery */
#include "epix.h"
using namespace ePiX;

int main()
{
double slope;
double c;
double x;

picture(P(-1.0,-1.0), P(1.0,1.0), "2.25x1.5in");

begin();

//h_axis(5);
//v_axis(5);

//h_axis_labels(3, P(-1, 2), tl); // align top-left
//v_axis_labels(3, P(-1, 2), tl);

pen(Black(0.4));
line_style(".");
dash_size(1);

bold();
line(P(-1,0),P(1,0));
line(P(0,-1),P(0,1));

plain();
line(P(-1,1),P(1,1));
line(P(0.5,-1),P(0.5,1));
line(P(-0.5,-1),P(-0.5,1));
line(P(1,-1),P(1,1));

solid();
pen(Black());

font_size("footnotesize");
bottom_axis(4, P(0,-4)).draw();
left_axis(2, P(-4,0)).draw();

bold();
line(P(-1,-1),P(1,1));
line(P(-1,1),P(1,-1));

tikz_format();
end();
}

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