On surfaces with $p_g=2$, $q=1$ and non-birational bicanonical map
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In the present note we show that any surface of general type with $p_g=2$,$q=1$ and non-birational bicanonical map has a pencil of curves of genus 2. Combining this result with previous ones, one obtains thatan irregular surface $S$ of general type with $χ(S)\geq 2$ and non-birational bicanonical map has a pencil of curves of genus 2.
Latex 2e, 10 pages. To appear in the Proceedings of the Conference in memory of Paolo Francia, Genova, September 2001
Latex 2e, 10 pages. To appear in the Proceedings of the Conference in memory of Paolo Francia, Genova, September 2001