Degeneration (algebraic geometry)

In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism π : X → C , {\displaystyle \pi :{\mathcal {X}}\to C,} of a variety (or a scheme) to a curve C with origin 0 (e.g., affine or projective line), the fibers π − 1 ( t ) {\displaystyle \pi ^{-1}(t)} form a family of varieties over C. Then the fiber π − 1 ( 0 ) {\displaystyle \pi ^{-1}(0)} may be thought of as the limit of π − 1 ( t ) {\displaystyle \pi ^{-1}(t)} as t → 0 {\displaystyle t\to 0} .

Source: Wikipedia — Degeneration (algebraic geometry) (CC BY-SA 4.0)