Mirror Symmetry Conjecture on Rational Curve

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Symplectic Language Theory

TANAKA Akio

   

Note3

Mirror Symmetry Conjecture on Rational Curve


[Conjecture]

Mirror relation     
  M, M^mir
  M is manifold.
  M^mir is 3-dimensional Calabi-Yau manifold.

Definition of Calabi-Yau manifold, the next is determined.



Yukawa combination
  

Mirror map Mir :
 
The upper's left is seemed as moduli space's tangent space at M's symplectic structure.


The next conjecture is satisfied.
 

The upper's right side is below.

F is Gromov-Witten potential.

[Note]

^₁

^{_{Actual language is given by manifold M.}}

^₂

_{^{Mirror language is given by Calabi-Yau manifold Mmir.}}

3

Deformation of M^mir is expressed by

 .

^₄

^{_{Relation between actual language and mirror language is given by the mirror map and the conjecture.}}

[References]

<Early papers on the theme>

#1 Guarantee of Language

#2 Mirror Language

#3 Actual Language and Imaginary Language

<Present consideration>

#4 twittersekinanlu

^{_{To be continued}}

^{_{Tokyo February 27, 2009}}

^{_{Sekinan Research Field of language}}

^{_{Back to sekinanlogoshome}}