| Abstract:
Desargues configurations in the plane depend on 11 degrees of freedom.
On the other hand, a conical sextuple (that is to say, a conic with six
points on it) also depends on 11 degrees of freedom. It is a theorem due
to Veronese that a conical sextuple gives rise to six Desargues
configurations. Using Gröbner bases, we will prove that this construction
is 'reversible' in the sense that a general Desargues configuration is
obtainable from six conical sextuples. Moreover, the Galois group
associated to this problem is isomorphic to the symmetric group on six
letters. No prior knowledge of any of the underlying geometric concepts
will be assumed.
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