Blowup of the plane in a point

by MOLabs
  • Full Color Sandstone

    Fully colored material with a coarse finish and a delicate feel.

    $42.84
Buy Now
One of the most important concepts in algebraic geometry and singularity theory is the blowup of a plane in the origin. The plane is mapped to a surface in 3-space in an interesting way: Every point of the plane outside the origin is mapped to a unique point of the surface above. But the origin itself is mapped to a whole line (the thick green one in the model) where each point on the line on the surface corresponds to a direction through the origin. In the model this is illustrated in the following way: The blue curve which passes twice through the origin in the plane is mapped to a blue curve in the surface, but the curve on the surface has no self-intersection because the two directions of the curve in the origin are mapped to different points of the green line above. See our youtube video on http://calendar.algebraicsurface.net/calendar.php?mode=youTube&day=09 for more information.

Dimensions

IN: 2.469 w x 2.469 d x 4.831 h
CM: 6.27 w x 6.27 d x 12.27 h

Comments

Sign In or Join to comment.
 
 
Logo

Hello.

We're sorry to inform you that we no longer support this browser and can't confirm that everything will work as expected. For the best Shapeways experience, please use one of the following browsers:

Click anywhere outside this window to continue.