Given a (complex) Abelian variety $ A $ a fixed dimension $ g $, To let $ d (A) $ Be the dimension of the smallest complex projective space in which it is embedded.
is $ d (A) $ uniform over all abelian varieties of a solid $ g $? Or are there special ones that can be embedded in even smaller projective rooms?
Can $ d (A) $ be calculated explicitly? I am especially interested in the case $ g = 2 $,