Mathematical Research Letters

Volume 8, Issue 1, January 2001 pp. 7-12.

A connectivity lemma for the Albanese map

Authors: M. Rovinsky
Author institution: Independent University of Moscow

Summary: 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.

Contents Full-Text PDF