### Abstract

In this paper we study principally polarized Abelian varieties that admit an automorphism of order 3. It turns out that certain natural conditions on the multiplicities of its action on the differentials of the first kind guarantee that those polarized varieties are not Jacobians of curves. As an application, we get another proof of the (already known) fact that intermediate Jacobians of certain cubic threefolds are not Jacobians of curves.

Original language | English (US) |
---|---|

Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 687-691 |

Number of pages | 5 |

DOIs | |

State | Published - Jan 1 2009 |

### Publication series

Name | Progress in Mathematics |
---|---|

Volume | 270 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Progress in Mathematics*(pp. 687-691). (Progress in Mathematics; Vol. 270). Springer Basel. https://doi.org/10.1007/978-0-8176-4747-6_23

}

*Progress in Mathematics.*Progress in Mathematics, vol. 270, Springer Basel, pp. 687-691. https://doi.org/10.1007/978-0-8176-4747-6_23

**Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians.** / Zarhin, Yuri.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians

AU - Zarhin, Yuri

PY - 2009/1/1

Y1 - 2009/1/1

N2 - In this paper we study principally polarized Abelian varieties that admit an automorphism of order 3. It turns out that certain natural conditions on the multiplicities of its action on the differentials of the first kind guarantee that those polarized varieties are not Jacobians of curves. As an application, we get another proof of the (already known) fact that intermediate Jacobians of certain cubic threefolds are not Jacobians of curves.

AB - In this paper we study principally polarized Abelian varieties that admit an automorphism of order 3. It turns out that certain natural conditions on the multiplicities of its action on the differentials of the first kind guarantee that those polarized varieties are not Jacobians of curves. As an application, we get another proof of the (already known) fact that intermediate Jacobians of certain cubic threefolds are not Jacobians of curves.

UR - http://www.scopus.com/inward/record.url?scp=84866009924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866009924&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-4747-6_23

DO - 10.1007/978-0-8176-4747-6_23

M3 - Chapter

AN - SCOPUS:84866009924

T3 - Progress in Mathematics

SP - 687

EP - 691

BT - Progress in Mathematics

PB - Springer Basel

ER -