Abstract
A d-dimensional normal projective variety X is called a Q-Fano d-fold if it has only terminal singularities and if the anti-canonical Weil divisor – Kx is ample. The singularity index I = I(X) of X is defined to be the smallest positive integer such that – IKX is Cartier. Then there is a positive integer r and a Cartier divisor H such that – IKX ~ rH. Taking the largest number of such r, we call r/I the Fano index of X.
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