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In mathematics, canonical singularities appear as singularities of the canonical model of a projective variety, and terminal singularities are special cases that appear as singularities of minimal models. They were introduced by . Terminal singularities are important in the minimal model program because smooth minimal models do not always exist, and thus one must allow certain singularities, namely the terminal singularities. ==Definition== Suppose that ''Y'' is a normal variety such that its canonical class ''K''''Y'' is Q-Cartier, and let ''f'':''X''→''Y'' be a resolution of the singularities of ''Y''. Then : where the sum is over the irreducible exceptional divisors, and the ''a''''i'' are rational numbers, called the discrepancies. Then the singularities of ''Y'' are called: :terminal if ''a''''i'' > 0 for all ''i'' :canonical if ''a''''i'' ≥ 0 for all ''i'' :log terminal if ''a''''i'' > −1 for all ''i'' :log canonical if ''a''''i'' ≥ −1 for all ''i''. See also: multiplier ideal (algebraic geometry). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「canonical singularity」の詳細全文を読む スポンサード リンク
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