Nagoya Mathematical Journal

On classification of $\mathbb{Q}$-Fano $3$-folds of Gorenstein index 2. II.

Hiromichi Takagi

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Abstract

In the previous paper, we obtained 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 $a \in \mathbb{N}$. Moreover we showed that such an $X$ is birational to a simpler Mori fiber space. In this paper, we prove their existence except for a few cases by constructing a Mori fiber space with desired properties and reconstructing $X$ from it.

Article information

Source
Nagoya Math. J., Volume 167 (2002), 157-216.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114649296

Mathematical Reviews number (MathSciNet)
MR1924722

Zentralblatt MATH identifier
1048.14023

Subjects
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Takagi, Hiromichi. On classification of $\mathbb{Q}$-Fano $3$-folds of Gorenstein index 2. II. Nagoya Math. J. 167 (2002), 157--216. https://projecteuclid.org/euclid.nmj/1114649296


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