Birational Language |
Birational Language
Elements of Word
1, Proposition
Weighted projective space
is birationally equivalent with projective space 
.
2. Proposition
Weighted hyperplane
is isomorphic to Weighted projective space .
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.
.
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 
.
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 .
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.
When elements of word is given at linear space, language is defined at projective space using birational equivalence.
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