A Universal Magnification Theorem III. Caustics Beyond Codimension Five

Abstract

In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.

8 pages

References in corpus (2)

• A Universal Magnification Theorem for Higher-Order Caustic Singularities
• A Universal Magnification Theorem II. Generic Caustics up to Codimension Five

Cited by in corpus (2)

• Signed magnification sums for general spherical lenses
• Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing