Degeneracy in geometric objects arises as a failure of structural maximality under defining morphisms. This white paper examines triangles and conics through categorical and functorial lenses, establishing unifying principles, structural distinctions, and implications for moduli space compactifications.
Degenerate triangles and conics are not analogous objects but analogous failures, manifesting as boundary points and singularities that reveal hidden algebraic structure.
Abstract
Degeneracy in geometric objects arises as a failure of structural maximality under defining morphisms. This white paper examines triangles and conics through categorical and functorial lenses, establishing unifying principles, structural distinctions, and implications for moduli space compactifications.
Degenerate triangles and conics are not analogous objects but analogous failures, manifesting as boundary points and singularities that reveal hidden algebraic structure.