ag.algebraic geometry – embedding abelian varieties in projective spaces of small dimension

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 $$g = 2$$,