Discrete line complexes and integrable evolution of minors

Abstract

Based on the classical Plücker correspondence, we present algebraic and geometric properties of discrete integrable line complexes in $C{P}^3$. Algebraically, these are encoded in a discrete integrable system which appears in various guises in the theory of continuous and discrete integrable systems. Geometrically, the existence of these integrable line complexes is shown to be guaranteed by Desargues' classical theorem of projective geometry. A remarkable characterisation in terms of correlations of $C{P}^3$ is also recorded.

29 pages, 11 figures; updated references

References in corpus (1)

• Hyperdeterminantal relations among symmetric principal minors

Cited by in corpus (4)

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• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations