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

Published online by Cambridge University Press:  22 January 2016

Takeshi Sano
Takeshi Sano*
Affiliation:
Graduate School of Polymathematics Nagoya University, Nagoya 464-01, Japan
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 142 , June 1996 , pp. 133 - 143
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

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