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On surfaces with $p_g=2$, $q=1$ and non-birational bicanonical map

Ciro Ciliberto·Margarida Mendes Lopes
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Abstract

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.

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Ciro Ciliberto, Margarida Mendes Lopes. 2002-03-01. On surfaces with $p_g=2$, $q=1$ and non-birational bicanonical map. https://arxiv.org/abs/math/0203007

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