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
Full-text PDF

Abstract | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

Additional Information

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

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2016 University Press, Inc.
AMS Website