Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Classification of primary $\mathbb {Q}$-Fano threefolds with anti-canonical Du Val $K3$ surfaces, I

Author: Hiromichi Takagi
Journal: J. Algebraic Geom. 15 (2006), 31-85
Published electronically: June 27, 2005
MathSciNet review: 2177195
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Abstract: If a non-Gorenstein $\mathbb {Q}$-Fano threefold with only cyclic quotient terminal singularities has anti-canonical Du Val $K3$ surfaces and the anti-canonical class generates the group of numerical equivalence classes of divisors, then the dimension of the space of global sections of the anti-canonical sheaf is shown to be not greater than ten. Such $\mathbb {Q}$-Fano threefolds with the dimension not less than nine are classified.

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Hiromichi Takagi
Affiliation: Graduate School of Mathematical Sciences, the University of Tokyo, Tokyo, 153-8914, Japan

Received by editor(s): June 17, 2004
Received by editor(s) in revised form: April 6, 2005, April 22, 2005, and May 12, 2005
Published electronically: June 27, 2005