Details:
Title  Cylinders through five points: Complex and real enumerative geometry.  Author(s)  Daniel Lichtblau  Type  Book, Chapter in Book, Conference Proceeding  Abstract  It is known that five points in ℝ3 generically determine a finite number of cylinders containing those points. We discuss ways in which it can be shown that the generic (complex) number of solutions, with multiplicity, is six, of which an even number will be real valued and hence correspond to actual cylinders in ℝ3. We partially classify the case of no real solutions in terms of the geometry of the five given points. We also investigate the special case where the five given points are coplanar, as it differs from the generic case for both complex and real valued solution cardinalities.  Keywords  Enumerative geometry, Gröbner bases, nonlinear systems  ISBN  9783540773559/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783540773566_6 
Language  English  Pages  8097  Publisher  Berlin: Springer  Year  2007  Edition  0  Translation 
No  Refereed 
No 
