Stucture of birational automorphism groups. I: Non-uniruled varieties (Q1112887)

In a previous paper [Compos. Math. 63, 123-142 (1987; Zbl 0655.14007)] the author introduced the notion of the scheme of birational automorphisms Bir(X) of an algebraic variety X. In good cases (B-good) \(Bir(X)_{red}\) is a group scheme which acts birationally on some model of X, and is universal among such group schemes. It was shown that minimal models are B-good. In the present paper the author verifies that any non-ruled variety is B- good. This agrees with a well-known conjecture that every non-ruled variety admits a minimal model. Other fundamental properties of Bir(X) verified in the case of minimal models are true also for non-ruled varieties. For instance, the author proves that dim(Bir(X))\(\leq \dim (X)\).