# SicMarcus

### Hand Made Fiducials By Tensoring

The file Media:FiducialsByTensoring.pdf consists of working notes for what will eventually be a published paper. It is work in progress, and so will be updated regularly. I will also attach a mathematica notebook giving the exact fiducial in dimension 6 in machine readable form, as soon as I can get the wiki to accept it (it is being recalcitrant at the moment).

The pdf concerns methods for obtaining exact fiducials in composite dimensions. It is based on David Gross's talk at the PI workshop in October 2008 (so it is joint work of David and myself). So far I have got as far as the exact solution in dimension 6. Of course Markus Grassl did this some years ago. However, the solution given here was obtained by *purely* pencil and paper methods (I used Mathematica to check the result, but in the original calculation I didn't even use Mathematica, let alone Magma).

I am currently working on dimension 12. I will then go on to dimension 15. I happen to know the method works in these dimensions because I had already obtained exact, pencil-and-paper solutions in these dimensions before hearing David's talk using a different, but related method (this different method also works in dimension 9, which David's method in the present formulation of it, does not. Another aim of this research is to clarify the exact relationship between David's method and the less elegant method I was using before).

Of course the real aim of all this is not just to find exact solutions, but to get enough algebraic insight into the problem to be able to construct a proof. In that respect I am feeling just a little bit hopeful. But it is very very slow (the algebra is really complicated!).