Syzygies of abelian varieties

Author:
Giuseppe Pareschi

Journal:
J. Amer. Math. Soc. **13** (2000), 651-664

MSC (2000):
Primary 14K05; Secondary 14F05

DOI:
https://doi.org/10.1090/S0894-0347-00-00335-0

Published electronically:
April 10, 2000

MathSciNet review:
1758758

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Abstract | References | Similar Articles | Additional Information

Abstract: 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 is an ample line on an abelian variety, then satisfies the property as soon as . 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:
pareschi@mat.uniroma2.it

DOI:
https://doi.org/10.1090/S0894-0347-00-00335-0

Keywords:
Homogeneous ideal,
Pontrjagin product,
vector bundles

Received by editor(s):
August 24, 1998

Received by editor(s) in revised form:
March 8, 2000

Published electronically:
April 10, 2000

Article copyright:
© Copyright 2000
American Mathematical Society