Meaning Minimum of Language / 5 October 2011

Stable and Unstable of Language

For the Supposition of KARCEVSKIJ Sergej

Meaning Minimum of Language

TANAKA Akio

[Preparation]

 ,

is graded ring and integral domain.

For negative e,  .

R's quotient field element is called homogenious when R's quotient field element is ratio f/g of homogenious element  .

Its degree is defined by .

<Definition>

At R's quotient field, subfield made by degree 0's whole homogenious elements,

 ,

is expressed by  .

For homogenious element  ,

subring of field  ,

 ,

is expressed by  .

For graded ring,

 ,

algebraic variety that  is quotient field that whole  for homogenious element  is gotten by gluing in common quotient field is expressed by Proj R.

Proj R of graded ring

,

 ,

is called projective algebraic variety.

<Conposition>

Projective algebraic variety is complete.

◊

<System>

Moduli of hypersurface,

,

is complete algebraic variety.

◊

 ,

is sum set of,

 ,  .

◊

[Interpretation]

Word is expressed by,

 .

Meaning minimum of word is expressed by,

,  .

For meaning minimum,

refer to the next.

[References]

• Cell Theory / From Cell to Manifold / Tokyo June 2, 2007
• Holomorphic Meaning Theory 2 / Tokyo June 19, 2008
• Amplitude of meaning minimum / Complex Manifold Deformation Theory / Conjecture A4 / Tokyo December 17, 2008
• Gromov-Witten Invariant / Symplectic Language Theory / Tokyo February 27,2009
• Generating Function / Symplectic Language Theory / Tokyo March 17, 2009

October 5, 2011

Sekinan Research Field of Language