A_6 is of general type -- Samuel Grushevsky, March 25, 2005

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We construct a new effective geometric divisor on A_g (the
moduli space of principally polarized complex abelian varieties) and use
it to show that A_6 is of general type. Since the work of Tai, Mumford,
Clemens, Donagi, etc. in the 1980s, this has remained the only g for which the
Kodaira dimension of A_g was unknown. This is joint work with David
Lehavi.