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| MY RESEARCH RELATED LINKS |
Barry H. Dayton Professor Emeritus |
MY OTHER WEB PAGES |
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Approximate local Rings (Paper presented at Notre Dame AMS meeting, April 9, 2006) Numerical Local Rings of Analytic Systems (January 2008)
Talk at ACA 2007
Talk at SNC 2007
Talk at Depaul AMS Meeting, October 2007
Preprint August 2008
Preprint January 2011
Preprint April 2011 SNC 2011 Talk on Numerical Calculation of H-bases... at ACM-FCRC conference, San Jose, CA, June 2011 (PDF slides) AG11 Talk on Numerical Algebraic Geometry at SIAM AG11 conference, Raleigh NC, October 2011 (PDF slides) Michigan Computational Algebraic Geometry talk on global duals at MCAG12, Oakland University, May 2012 (PDF slides). SIAM talk on Numerical Algebraic Geometry via Macaulay at Numerical Methods for Polynomial Systems, AN12, Minneapolis, July 2012 (PDF slides). |
Lines in a cubic Surface![]() In 1849 Salmon and Caley discovered that there are exactly 27 straight lines contained in a non-singular complex projective cubic in 3-space. Unfortunately it is not easy to show these in Euclidean 3-space, some of these lines may lie in the plane at infinity and most of these lines generally are complex. For example, the Fermat cubic specializes to the cubic
In 1856 in an attempt to clarify the Salmon-Caley result Ludwig Schlaefli gave a construction of 12 lines that would lie in a cubic. The resulting set of lines is now known as "Schlaefli's double 6." It is easy from these to find the remaining 15 lines. These lines can be chosen, with care, to be real. Hilbert included this construction in his popular book on geometry "Geometry and the Imagination" written with S. Cohn-Vossen in 1932. This book is presently available from the American Mathematical Society The paper Numerical Calculation of H-bases for Positive Dimensional Varieties discusses lines in the cubic from an affine (non-projective) point of view. |
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Home Page of Barry H Dayton Professor Emeritus Northeastern Illinois University Chicago, IL 60625-4699, USA B-Dayton@neiu.edu |