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Language has stability.
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Stability is defined by the following.
From KAWAMATA Yujiro, Stab X that consists of the set having all <locally finite> and <numerical> <stability condition> on derived category D(X) has finite dimensional complex manifold’s structure. Stab (X) is conjectured to beconnected and simply connected. In derived category, exact sequence is extinct and distinguished triangle is generated.
Refer to the next paper. KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1 Iwanami Shoten 2006
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Now blow up and blow down is presented.
φ: QY(M) → M
M is nonsingular variety. Y is M’s submanifold.
QY(M) is blow up along Y.
φis arrow of algebraic variety
φis called QY(M)’s blow down.
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Also birational mapping that is extension of blow up and blow down is presented.
Birational mapping is what rational mappingφ: V→W has mapping ψ: W→V. Here existsφ∘ψ= idV ψ∘φ=idW .
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By birational mapping, algebraic variety V, W and X is presented. These three are formed to be new distinguished triangle that is supposed to be equivalent with V, W and X.
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Word that consists of category makes sentence that consists of distinguished triangle by birational mapping with algebraic method.
Tokyo April 30, 2007
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