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On classification of ℚ-fano 3-folds of Gorenstein index 2. I

Published online by Cambridge University Press:  22 January 2016

Hiromichi Takagi
Hiromichi Takagi*
Affiliation:
RIMS, Kyoto University, Kitashirakawa Sakyo-ku Kyoto, 606-8502, Japan, takagi@kurims.kyoto-u.ac.jp
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Abstract

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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 ℚ-Fano 3-folds X with Pic X = ℤ(−2KX) and h0(−KX) ≥ 4 containing index 2 points P such that (X, P) ≃ ({xy + z2 + ua = 0}/ℤ2(1, 1, 1, 0), o) for some a ∈ ℕ. In particular we prove that then (–KX)3 ≤ 15 and h0(–KX) ≤ 10. Moreover we show that such an X is birational to a simpler Mori fiber space.

Keywords

14J4514N0514M20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 167 , 2002 , pp. 117 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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