Systems of conservation laws in the setting of the projective theory of congruences: reducible and linearly degenerate systems

AbstractWe review some of the recent results in the projective-geometric theory of systems of conservation laws with emphasis on linearly degenerate systems, reducible systems and systems of Temple's class, the equations of associativity of two-dimensional topological field theory being the main example. Our construction reveals a close relationship of these classes of systems with linear congruences and linear complexes of lines in projective space