Duality of Language. The latest paper of Derived Category Language

Duality of Language

TANAKA Akio

1. Model
Calabi-Yau 3-folds.

2. Theorem
R. Pandharipande and R.P. Thomas.  
Pandharipande-Thomas Theorem (1998).
K. Behrend.
Behrent contructable function (2009).

Y. Toda.
Generating functions of stable pair invariants via wall-crossing in derived categories in algebraic geometry. (2008)
Curve-counting theories via stable objects (2010).
T. Bridgeland.
Hall algebras and curve-counting invariants (2011).
D. Joyce and Y.Song.
A theory of generalized Donaldson-Thomas invariants. (2012)

3. Definition
Generalized DT invariants. ( Joyce and Song. 2012)

4. Isomorphism
Isomorphism is induced in the defined moduli spaces.

5. Duality and mirror
If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.

Reference
Rensetsuso no Doraiken ni kakawaru shomondai. TODA Yukinobu. 2016. Sugaku shobo. Tokyo.

Reference 2
Derived Category Language, 25 May 2016 Edition.

Reference 3.
Actual Language and Imaginary Language. To LÉVI-STRAUSS Claude.

Reference 4.
Symplectic Language Theory ​ Note 3 Mirror Symmetry Conjecture on Rational Curve​.
Symplectic Language Theory ​ Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH​.

Reference 5.
Main papers of Sekinan Library.
SRFL Paper.

Paper ends. 
-----------------------------------------------------------------------------------------------------------------------

This paper is unfinished.

Tokyo
22 July 2016
Sekinan Library