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arXiv · 1604.00050

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

A. Huitrado-Mora·M. Castaneda-Salazar·A. G. Zamora
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Abstract

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.

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A. Huitrado-Mora, M. Castaneda-Salazar, A. G. Zamora. 2016-03-31. Toward a conjecture of Tan and Tu on fibered general type surfaces. https://arxiv.org/abs/1604.00050

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