Abstract: We construct new effective geometric divisors on the moduli spaces A_g of principally polarized complex abelian varieties. For g >= 5 we obtain a divisor of slope smaller than the currently known minimum. This in particular allows us to prove that A_g is of general type for g >= 6, thus settling the case of the Kodaira dimension of A_6 --- since the 1980s the only dimension for which it has been unknown.

This is joint work with S. Grushevsky.