Corpus ID: 119140728

Toward a conjecture of Tan and Tu on fibered general type surfaces

@article{HuitradoMora2016TowardAC,
  title={Toward a conjecture of Tan and Tu on fibered general type surfaces},
  author={Huitrado-Mora and A. and Castaneda-Salazar and M. and Zamora and G. A.},
  journal={arXiv: Algebraic Geometry},
  year={2016}
}
Given a semistable non-isotrivial fibered surface $f:X\to \mathbb{P}^1$ it was conjectured by Tan and Tu that if $X$ is of general type, then $f$ admits at least $7$ singular fibers. In this paper we prove this conjecture in several particular cases, i.e. assuming $f$ is obtained from blowing-up the base locus of a transversal pencil on an exceptional minimal surface $S$ or assuming that $f$ is obtained as the blow-up of the base locus of a transversal and adjoint pencil on a minimal surface. 
Singular fibers and Kodaira dimensions
Let $$f:\,X \rightarrow \mathbb {P}^1$$f:X→P1 be a non-isotrivial semi-stable family of varieties of dimension m over $$\mathbb {P}^1$$P1 with s singular fibers. Assume that the smooth fibers F areExpand

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