Abstracts for Conference in Memory of Yuri Manin

Semi-infinite Hodge structure equipped with primitive forms is constructed for hyperbolic root systems of rank 2. As the consequences, we determine (1) the flat structure and the Frobenius manifold structure and (2) the ''virtual'' period maps for the primitive forms.

We study principally polarized complex abelian varieties $(X,\lambda)$ of positive dimension $g$ that admit an automorphism $\delta$ of prime order $p>2$, whose set of fixed points $X^{\delta}$ is finite.  Such triples $(X,\lambda,\delta)$ exist if and only if $(p-1)$ divides $2g$.