Fano Varieties and Extremal Laurent Polynomials

Below are animations showing some of the shapes that we have analyzed in our project so far.  Please email me if you need higher or lower resolution versions.  An explanation of what the animations show is here.

• Animation 1: slices of the Fano variety seen from several different angles.  Hi-res version. Low-res version.
  

  
  

• Animation 2: slices of the Fano variety seen from two different angles.  Hi-res version. Low-res version.
  
  
• Animation 3: the cubic threefold, seen from the outside from various angles.  Hi-res version.
  
  
• Animation 4: the cubic threefold and slices through it.  Hi-res version. Low-res version.
  
  
• Animation 5: breaking up a shape into simpler pieces.  This animation shows how a surface called a hyperboloid (the curved cylinder) is made up from straight lines (shown in red).  You can think of the hyperboloid as a “molecule”, made up from “atoms” that are the straight lines.  Hi-res version. Low-res version.