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

A. Huitrado-Mora; M. Castaneda-Salazar; A. G. Zamora

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

Algebraic Geometry 2025-10-09 v1

Authors: A. Huitrado-Mora , M. Castaneda-Salazar , A. G. Zamora

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.

Keywords

fibered general type surface Tan-Tu conjecture singular fibers semistable non-isotrivial fibration blowing-up pencil minimal surface

Cite

@article{arxiv.1604.00050,
  title  = {Toward a conjecture of Tan and Tu on fibered general type surfaces},
  author = {A. Huitrado-Mora and M. Castaneda-Salazar and A. G. Zamora},
  journal= {arXiv preprint arXiv:1604.00050},
  year   = {2025}
}

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

Abstract

Keywords

Cite

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