References:

• Yuri Prokhorov. Q-Fano threefolds of large Fano index, I. arXiv:0812.1695
• Yuri Prokhorov. The degree of Q-Fano threefolds. math/0610026

Рari source code for finding Fano 3-folds with at worst terminal singularities of Fano index >2. The user can specify the degree, anticanonical dimension, Fano index, etc.

• create_list_baskets.gp The program creates a list of possible baskets of all Fano 3-folds with terminal singularitis. The results are sent to list_baskets.out
• create_list_q_ge3.gp Using list_baskets.out, the program creates a list of possible baskets of all Fano 3-folds with with terminal singularitis of Fano index >3. The results are sent to the file list_fano_ge3.out.
• seach_fano_q_ge3.gp It searches in list_fano_ge3.out Fanos with specified parameters.

List of posssible candidates (it does not include Gorenstein Fano 3-folds)

• Fano 3-folds of index qW=3
• Fano 3-folds of index qW=4
• Fano 3-folds of index qW=5
• Fano 3-folds of index qW=6
• Fano 3-folds of index qW=7
• Fano 3-folds of index qW=8
• Fano 3-folds of index qW\ge 9

Other data and databases:

• Graded Ring Database
• Calabi-Yau data

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