BIRATIONAL COMPOSITION OF QUADRATIC FORMS OVER A FUNCTION FIELD
Abstract
Let ƒ(X) and g(Y) be nonsingular quadratic forms over a field K having dimensions m and n , charK≠ 2. The following problem of a birational compositions ƒ(X) and g(Y)is considered: under which conditions is the product ƒ(X) and g(Y)birationally equivalent over K to a quadratic form h(Z) of dimension m+n over K?
The main result of the paper is a complete solution of the birational composition problem for quadratic forms ƒ(X) and g(Y)over the function field F, char F ≠ 2.
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