## Title data

Dettweiler, Michael ; Catanese, Fabrizio:

**Vector bundles on curves coming from variation of Hodge structures.**

*In:* International Journal of Mathematics.
Vol. 27
(2016)
Issue 7
.
- 1640001.

ISSN 1793-6519

DOI: https://doi.org/10.1142/S0129167X16400012

Review: |

## Abstract in another language

Fujita’s second theorem for Kähler fibre spaces over a curve asserts, that the direct image V of the relative dualizing sheaf splits as the direct sum V=A⊕Q, where A is ample and Q is unitary flat. We focus on our negative answer [F. Catanese and M. Dettweiler, Answer to a question by Fujita on variation of Hodge structures, to appear in Adv. Stud. Pure Math.] to a question by Fujita: is V semiample? We give here an infinite series of counterexamples using hypergeometric integrals and we give a simple argument to show that the monodromy representation is infinite. Our counterexamples are surfaces of general type with positive index, explicitly given as abelian coverings with group (Z/n)2 of a Del Pezzo surface Z of degree 5 (branched on the union of the lines of Z, which form a bianticanonical divisor), and endowed with a semistable fibration with only three singular fibres. The simplest such surfaces are the three ball quotients considered in [I. C. Bauer and F. Catanese, A volume maximizing canonical surface in 3-space, Comment. Math. Helv.83(1) (2008) 387–406.], fibred over a curve of genus 2, and with fibres of genus 4. These examples are a larger class than the ones corresponding to Shimura curves in the moduli space of Abelian varieties.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Relative dualizing sheaf; semiamplenett; monodromy; semistable fibration |

Subject classification: | Mathematics Subject Classification 2010: 14D0, 14C30, 32G20, 33C60 |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics IV (Number Theory) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics IV (Number Theory) > Chair Mathematics IV (Number Theorie) - Univ.-Prof. Dr. Michael Dettweiler |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 05 May 2023 10:25 |

Last Modified: | 03 Aug 2023 13:33 |

URI: | https://eref.uni-bayreuth.de/id/eprint/75961 |