Birational Language Elements of Word 2012

 

Birational Language

Elements of Word

TANAKA Akio

1, Proposition
Weighted projective space  is birationally equivalent with projective space  .

2. Proposition
Weighted hyperplane  is isomorphic to Weighted projective space  .

3. Proposition
Weighted projective space  is one-to-one correspondent with quotient space  .
Here G is finite Abellian group to ptrojective space .
 .

4. Definition
The next  is hyperplane defined by equation  .
 .
Here coordinate system  of linear space V is called homogenious coordinate system of projective space  .

5. Interpretation
Language:= projective space  .
Word:=Weighted hyperplane  .
Elements of word:=coordinate system  of linear space V .

6. Conclution
When elements of word is given at linear space, language is defined at projective space using birational equivalence.

7. Reference
Grassmann Language 2 / Elements of Word / April 11, 2012

Tokyo
April 26, 2012
Sekinan Research Field of Language