Basepoint-freeness thresholds and higher syzygies on abelian threefolds

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For a polarized abelian variety, Z. Jiang and G. Pareschi introduced an invariant and showed that the polarization is basepoint-free or projectively normal if the invariant is small. Their result was generalized to higher syzygies by F. Caucci; that is, the polarization satisfies property (Np) if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we armatively answer some questions on abelian varieties asked by the author, V. Lozovanu and F. Caucci in the three-dimensional case.

Original languageEnglish
Pages (from-to)762-787
Number of pages26
JournalAlgebraic Geometry
Issue number6
Publication statusPublished - Nov 2022
Externally publishedYes


  • Abelian variety
  • Basepoint-freeness threshold.
  • Syzygy

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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