On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety

摘要: To any closed subvariety Y of a complex abelian variety one can attach reductive algebraic group G which is determined by the decomposition convolution powers via certain Tannakian formalism. For theta divisor on principally polarized variety, this provides new invariant that naturally endows moduli space \({{\mathcal {A}}}_g\) varieties dimension g with finite constructible stratification. We determine for generic and \(g=4\) we show stratification detects locus Jacobian inside varieties.