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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Syzygies of abelian varieties
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by Giuseppe Pareschi PDF
J. Amer. Math. Soc. 13 (2000), 651-664 Request permission


We prove a conjecture of R. Lazarsfeld on the syzygies (of the homogeneous ideal) of abelian varieties embedded in projective space by multiples of an ample line bundle. Specifically, we prove that if $A$ is an ample line on an abelian variety, then $A^{\otimes n}$ satisfies the property $N_{p}$ as soon as $n\ge p+ 3$. The proof uses a criterion for the global generation of vector bundles on abelian varieties (generalizing the classical one for line bundles) and a criterion for the surjectivity of multiplication maps of global sections of two vector bundles in terms of the vanishing of the cohomology of certain twists of their Pontrjagin product.
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Additional Information
  • Giuseppe Pareschi
  • Affiliation: Dipartimento di Matematica, Università di Roma, Tor Vergata V.le della Ricerca Scientifica, I-00133 Roma, Italy
  • Email:
  • Received by editor(s): August 24, 1998
  • Received by editor(s) in revised form: March 8, 2000
  • Published electronically: April 10, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 13 (2000), 651-664
  • MSC (2000): Primary 14K05; Secondary 14F05
  • DOI:
  • MathSciNet review: 1758758