Syzygies of abelian varieties

@inproceedings{Pareschi2000SyzygiesOA,
  title={Syzygies of abelian varieties},
  author={Giuseppe Pareschi},
  year={2000}
}
Let A be an ample line bundle on an abelian varietyX (over an algebraically closed field). A theorem of Koizumi ([Ko],[S]), developing Mumford’s ideas and results in [M1], states that if m ≥ 3 the line bundle L = A⊗m embeds X in projective space as a projectively normal variety. Moreover, a celebrated theorem of Mumford ([M2]), slightly refined by Kempf ([K4]), asserts that the homogeneous ideal of X is generated by quadrics as soon as m ≥ 4. Such results turn out to be particular cases of a… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 13 references

Koszul cohomology and the geometry of projective varieties I

  • M. Green
  • J. Diff. Geom
  • 1984
Highly Influential
10 Excerpts

Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension

  • L. EL Ein, R. Lazarsfeld
  • Inv. Math
  • 1993

Complex abelian varieties and theta functions, Springer-Verlag

  • G. Kempf
  • 1990

A sampling of vector bundles techniques in the study of linear series

  • R. Lazarsfeld
  • Lectures on Riemann surfaces, World Scientific
  • 1989

Koszul cohomology and geometry

  • M. Green
  • Lectures on Riemann surfaces, World Scientific
  • 1989

Linear systems on abelian varieties

  • G. Kempf
  • Am. J. Math
  • 1989

Projective coordinate rings of abelian varieties, in : Algebraic analysis, geometry and number theory, J.I.Igusa ed

  • G. Kempf
  • 1989

Multiplication over abelian varieties

  • G. Kempf
  • Am. J. Math
  • 1988

Duality between D(X) and D(X̂) with its application to Picard sheaves

  • S. Mu Mukai
  • Nagoya Math.J
  • 1981

Toward the inversion of abelian integrals I

  • G. Kempf
  • Ann. Math
  • 1979

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