About: Degeneration (algebraic geometry)

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In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism of a variety (or a scheme) to a curve C with origin 0 (e.g., affine or projective line), the fibers form a family of varieties over C. Then the fiber may be thought of as the limit of as . One then says the family degenerates to the special fiber . The limiting process behaves nicely when is a flat morphism and, in that case, the degeneration is called a flat degeneration. Many authors assume degenerations to be flat.

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  • In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism of a variety (or a scheme) to a curve C with origin 0 (e.g., affine or projective line), the fibers form a family of varieties over C. Then the fiber may be thought of as the limit of as . One then says the family degenerates to the special fiber . The limiting process behaves nicely when is a flat morphism and, in that case, the degeneration is called a flat degeneration. Many authors assume degenerations to be flat. When the family is trivial away from a special fiber; i.e., is independent of up to (coherent) isomorphisms, is called a general fiber. (en)
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  • In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism of a variety (or a scheme) to a curve C with origin 0 (e.g., affine or projective line), the fibers form a family of varieties over C. Then the fiber may be thought of as the limit of as . One then says the family degenerates to the special fiber . The limiting process behaves nicely when is a flat morphism and, in that case, the degeneration is called a flat degeneration. Many authors assume degenerations to be flat. (en)
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  • Degeneration (algebraic geometry) (en)
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