V. Guletskii: The middle of the diagonal of a surface with $p_g=0$ and $q=1$

guletskii@im.bas-net.by

Submission: 2000, Apr. 17

We prove that if $X$ is a smooth projective complex surface with the invariants $p_g=0$ and $q=1$ then the middle Murre projector $\pi _2$ (see \cite{Mu} or \cite{Sch} for the definition of $\pi _2$) can be generated by two natural divisors on $X$ whose cohomology classes form a basis for the second cohomology group $H^2(X,\mathbb Q)$. As a consequence, this provides a second, in fact, Chow-motivic, proof of the triviality of the Albanese kernel for surfaces with $p_g=0$ and $q=1$ (the first proof was made in \cite{BKL}).

1991 Mathematics Subject Classification:

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