Syzygies of abelian varieties

  title={Syzygies of abelian varieties},
  author={Giuseppe Pareschi},
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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