Computational algebraic geometry of projective configurations

AbstractThis article deals with algorithmic and structural aspects related to the computer-aided study of incidence configurations in plane projective geometry. We describe invariant-theoretic algorithms and complexity results for computing the realization space and deciding the coordinatizability of configurations. A practical procedure for automated theorem proving in projective geometry is obtained as a special case. We use the final polynomial technique of Bokowski and Whiteley for encoding the resulting proofs, and we apply Buch-berger's Gröbner basis method for computing minimum degree final polynomials and final syzygies, thus attaining the bounds in the recent effective versions of Hubert's Nullstellen-satz