Mathematical Research Letters
Volume 8 (2001)
A connectivity lemma for the Albanese map
Pages: 7 – 12
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.