Saturday 29 December 2018

Language and Spacetime Stability of Language 2007


Stability of Language


1
Language has stability.
2
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(Xhas finite dimensional complex manifold’s structure. Stab (X) is conjectured to be connected 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
3
Now blow up and blow down is presented.
φ: QY(M) → M
M is nonsingular variety. is M’s submanifold.
QY(M) is blow up along Y.
φis arrow of algebraic variety
φis called QY(M)’s blow down.
4
Also birational mapping that is extension of blow up and blow down is presented.
Birational mapping is what rational mappingφ: V has  mapping ψ: WV.     Here existsφ∘ψ= idV ψ∘φ=idW .
5
By birational mapping, algebraic variety VW and X is presented. These three are formed to be new distinguished triangle that is supposed to be equivalent with Vand X.
6
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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