Mathematical Research Letters

Volume 8 (2001)

Number 1

A connectivity lemma for the Albanese map

Pages: 7 – 12



M. Rovinsky (Independent University of Moscow)


I show that for any complex projective variety $X$ and a sufficiently large integer $N$ all the fibers of Albanese map of the $N$-th symmetric power of $X$ are dominated by connected projective varieties with vanishing $H^1$. This result reduces certain problems on 0-cycles on smooth varieties to those on smooth surfaces with vanishing $H^1$'s.

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