## Title data

Catanese, Fabrizio:

**General birationality and hyperelliptic theta divisors.**

*In:* Annali di Matematica Pura ed Applicata.
(25 June 2024)
.

ISSN 1618-1891

DOI: https://doi.org/10.1007/s10231-024-01473-9

## Abstract in another language

We first state a condition ensuring that having a birational map onto the image is an open property for families of irreducible normal non uniruled varieties. We give then some criteria to ensure general birationality for a family of rational maps, via specializations. Among the applications is a new proof of the main result of Catanese and Cesarano (Electron Res Arch 29(6):4315–4325, 2021) that, for a general pair (A, X) of an (ample) Hypersurface X in an Abelian Variety A, the canonical map $$\Phi _X$$of X is birational onto its image if the polarization given by X is not principal. The proof is also based on a careful study of the Theta divisors of the Jacobians of Hyperelliptic curves, and some related geometrical constructions. We investigate these here also in view of their beauty and of their independent interest, as they lead to a description of the rings of Hyperelliptic theta functions.

## Further data

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

Refereed: | Yes |

Keywords: | Birational maps; Hypersurfaces in Abelian varieties; Canonical maps; Gauss maps; Theta divisors; Hyperelliptic curves; Graded rings of theta functions |

Subject classification: | 14E05; 14E25; 14M99; 14K25; 14K99; 14H40; 32J25; 32Q55; 32H04 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Chair Mathematics VIII (Algebraic Geometry) - Univ.-Prof. Dr. Fabrizio Catanese 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 > Former Professors |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 19 Oct 2024 21:00 |

Last Modified: | 21 Oct 2024 09:39 |

URI: | https://eref.uni-bayreuth.de/id/eprint/90769 |