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Canonical classes and
the geography of nonminimal Lefschetz fibrations over
S2
Yoshihisa Sato |
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Vol. 262 (2013), No. 1, 191–226
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Abstract |
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The Stipsicz conjecture on the fiber-sum decomposability of Lefschetz fibrations states that nonminimal Lefschetz fibrations over S2 are irreducible with respect to fiber-sum decompositions and we can judge that such Lefschetz fibrations are prime and fundamental. In this paper, we can determine the canonical classes of nonminimal Lefschetz fibrations admitting spheres of square −1 whose total intersection number with generic fiber is big. As a consequence, we consider the Kodaira dimension and the geography problem of such Lefschetz fibrations. |
Keywords
Lefschetz fibrations, canonical class, geography,
4-manifolds, pseudoholomorphic curves, Gromov invariants
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Mathematical Subject Classification 2010
Primary: 14J80, 57R17
Secondary: 14D06, 32Q65
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Milestones
Received: 3 August 2011
Revised: 11 July 2012
Accepted: 6 November 2012
Published: 27 March 2013
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Authors |
| Yoshihisa Sato | |
| Department of Systems Design and
Informatics Kyushu Institute of Technology 680-4 Kawazu, Iizuka Fukuoka 820-8502 Japan |
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