On Classification of Q-fano 3-folds of Gorenstein Index 2

@inproceedings{Takagi2007OnCO,
  title={On Classification of Q-fano 3-folds of Gorenstein Index 2},
  author={Hiromichi Takagi},
  year={2007}
}
We formulate a generalization of K. Takeuchi’s method to classify smooth Fano 3-folds and use it to give a list of numerical possibilities of QFano 3-folds X with Pic X = Z(−2KX) and h(−KX) ≥ 4 containing index 2 points P such that (X, P ) ≃ ({xy + z + u = 0}/Z2(1, 1, 1, 0), o) for some a ∈ N. In particular we prove that then (−KX) ≤ 15 and h(−KX) ≤ 10. Moreover we show that such an X is birational to a simpler Mori fiber space. 
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