MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $A$ be an abelian variety of dimension g and a polarization $L$ of type $(d_1,.....,d_g)$ (let alone the case $d_i=d_j,$ $\forall i, j$). What is the degree of the generators of the homogeneous ideal of A projectively embedded via the sections of L?

I know that Gross and Popescu gave results for surfaces with L of type $(1,d)$ - for instance if $d>10$ the ideal is generated by quadrics - but what for other polarizations and most of all for higher dimensions? Is this known?

share|cite|improve this question

Though I don't have enough details to really write it out here, you'll be wanting to look at Mumford's "On the Equations Defining Abelian Varieties I, II, III", which are in volume I of his selected papers (as well as his website at the links provided), and also the wikipedia page here.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.