20080912, 16:36  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
14356_{8} Posts 
Small problem in sixdimensional space
I'm considering the codimension1inP5object defined by
x^6+y^6+z^6 = u^6+v^6+w^6 with the obvious solutionsbypermutation removed and GCD(x,y,z,u,v,w)=1. I've searched for z,w<2000, and am finding that the number of these points with z,w<N seems to be slightly more than linear in N, so I suspect there are some families of points lurking. Suspiciously many of the points I've found have x+y+u=z+v+w, for example. http://www.jstor.org/pss/2005335 gives a set of homogeneous quartics parameterising some solutions, but clearly not all solutions since the quartics happen also to satisfy x^2+y^2+z^2=u^2+v^2+w^2. What are the right sort of questions to ask about the set of points on a highdimensional variety? 
20080913, 06:03  #2  
Nov 2003
1110100100100_{2} Posts 
Quote:
What does the jinvariant look like? Is the variety even Abelian? How many localizations yield singularities? (i.e. how many primes have bad reduction) 

20080913, 06:07  #3  
Nov 2003
16444_{8} Posts 
Quote:
genus? i.e. if viewed as a Riemann surface over C, how many holes does the surface have? Then one might study conformal maps of that surface. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Space Man  storm5510  Lounge  8  20170401 22:07 
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve  mickfrancis  Factoring  2  20160506 08:13 
Dimensional analysis  davieddy  Puzzles  9  20110802 09:59 
Clusters! In! Space!  CRGreathouse  Information & Answers  29  20110502 04:33 
Small FFTs vs. Blend Crash Problem  MoeStooge  Hardware  40  20040208 18:57 