Classification of non-Gorenstein Q -Fano d -folds of Fano index greater than d − 2

Source 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 – K x is ample. The singularity index I = I(X) of X is defined to be the smallest positive integer such that – IK X is Cartier. Then there is a positive integer r and a Cartier divisor H such that – IK X ~ rH . Taking the largest number of such r , we call r/I the Fano index of X .