A pr 2 00 0 BOUND OF AUTOMORPHISMS OF PROJECTIVE VARIETIES OF GENERAL TYPE Hajime TSUJI April , 2000

We prove that there exists a positive integer Cn depending only on n such that for every smooth projective n-fold of general type X defined over C, the automorphism group Aut(X) of X satisfies ♯Aut(X) ≤ Cn · μ(X,KX ), where μ(X,KX ) is the volume of X with respect to KX . MSC14E05,32J25.