Birational Language

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 .
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4. Definition
The next is hyperplane defined by equation .
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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 Reserach Field of Language