Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages687-691
Number of pages5
DOIs
StatePublished - Jan 1 2009

Publication series

NameProgress in Mathematics
Volume270
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Fingerprint

Cubic Surface
Threefolds
Curve
Abelian Variety
Automorphism
Multiplicity

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Zarhin, Y. (2009). Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians. In Progress in Mathematics (pp. 687-691). (Progress in Mathematics; Vol. 270). Springer Basel. https://doi.org/10.1007/978-0-8176-4747-6_23
Zarhin, Yuri. / Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians. Progress in Mathematics. Springer Basel, 2009. pp. 687-691 (Progress in Mathematics).
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Zarhin, Y 2009, Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians. in 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.

Progress in Mathematics. Springer Basel, 2009. p. 687-691 (Progress in Mathematics; Vol. 270).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Zarhin Y. Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians. In Progress in Mathematics. Springer Basel. 2009. p. 687-691. (Progress in Mathematics). https://doi.org/10.1007/978-0-8176-4747-6_23