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2002 On classification of $\mathbb{Q}-Fano 3-folds of Gorenstein index 2. I
Hiromichi Takagi
Nagoya Math. J. 167(none): 117-155 (2002).

Abstract

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 $\mathbb{Q}$-Fano $3$-folds $X$ with Pic $X = \mathbb{Z} (-2K_{X})$ and $h^{0} (-K_{X}) \geq 4$ containing index $2$ points $P$ such that $(X, P) \simeq (\{xy +z^{2}+u^{a}=0\} / \mathbb{Z}_{2}(1, 1, 1, 0), o)$ for some $a \in \mathbb{N}$. In particular we prove that then $(-K_{X})^{3} \leq 15$ and $h^{0} (-K_{X}) \leq 10$. Moreover we show that such an $X$ is birational to a simpler Mori fiber space.

Citation

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Hiromichi Takagi. "On classification of $\mathbb{Q}-Fano 3-folds of Gorenstein index 2. I." Nagoya Math. J. 167 117 - 155, 2002.

Information

Published: 2002
First available in Project Euclid: 27 April 2005

zbMATH: 1048.14022
MathSciNet: MR1924722

Subjects:
Primary: 14J45
Secondary: 14E05, 14E30, 14J30

Rights: Copyright © 2002 Editorial Board, Nagoya Mathematical Journal

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Vol.167 • 2002
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