Why the function field of an algebraic curve $f(x,y)=0$ can be identified with $overlineL(x)[y]/(f)$?
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I am reading the paper An algorithm for computing the Weierstrass normal form. I have a question about the function field of an algebraic curve.
Let $f(x,y)$ be a polynomial in $x,y$. Let $L$ be the field generated by the coefficients of $f$. Let $C$ be the curve given by $f(x,y)=0$.
On page 2, Section 2, it is said that the function field $overlineL(C)$ can be identified with $overlineL(x)[y]/(f)$.
How to prove this fact? Thank you very much.
algebraic-geometry commutative-algebra
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I am reading the paper An algorithm for computing the Weierstrass normal form. I have a question about the function field of an algebraic curve.
Let $f(x,y)$ be a polynomial in $x,y$. Let $L$ be the field generated by the coefficients of $f$. Let $C$ be the curve given by $f(x,y)=0$.
On page 2, Section 2, it is said that the function field $overlineL(C)$ can be identified with $overlineL(x)[y]/(f)$.
How to prove this fact? Thank you very much.
algebraic-geometry commutative-algebra
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am reading the paper An algorithm for computing the Weierstrass normal form. I have a question about the function field of an algebraic curve.
Let $f(x,y)$ be a polynomial in $x,y$. Let $L$ be the field generated by the coefficients of $f$. Let $C$ be the curve given by $f(x,y)=0$.
On page 2, Section 2, it is said that the function field $overlineL(C)$ can be identified with $overlineL(x)[y]/(f)$.
How to prove this fact? Thank you very much.
algebraic-geometry commutative-algebra
I am reading the paper An algorithm for computing the Weierstrass normal form. I have a question about the function field of an algebraic curve.
Let $f(x,y)$ be a polynomial in $x,y$. Let $L$ be the field generated by the coefficients of $f$. Let $C$ be the curve given by $f(x,y)=0$.
On page 2, Section 2, it is said that the function field $overlineL(C)$ can be identified with $overlineL(x)[y]/(f)$.
How to prove this fact? Thank you very much.
algebraic-geometry commutative-algebra
asked Aug 23 at 8:40
LJR
6,47041646
6,47041646
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