Mathematical Research Letters

Volume 8 (2001)

Number 1

A connectivity lemma for the Albanese map

Pages: 7 – 12

DOI: http://dx.doi.org/10.4310/MRL.2001.v8.n1.a2

Author

M. Rovinsky (Independent University of Moscow)

Abstract

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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