Duality of Language
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.
Read more: http://srfl-paper.webnode.com/news/duality-of-language-derived-category-language/
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