Open Access
Translator Disclaimer
2002 On classification of $\mathbb{Q}$-Fano $3$-folds of Gorenstein index 2. II.
Hiromichi Takagi
Nagoya Math. J. 167: 157-216 (2002).

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.

Citation

Download Citation

Hiromichi Takagi. "On classification of $\mathbb{Q}$-Fano $3$-folds of Gorenstein index 2. II.." Nagoya Math. J. 167 157 - 216, 2002.

Information

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

zbMATH: 1048.14023
MathSciNet: MR1924722

Subjects:
Primary: 13D45
Secondary: 13C15 , 13H10

Rights: Copyright © 2002 Editorial Board, Nagoya Mathematical Journal

JOURNAL ARTICLE
60 PAGES


SHARE
Vol.167 • 2002
Back to Top