On surfaces with ${p}_{g}=q=1$ and non-ruled bicanonical involution
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, p. 81-102

This paper classifies surfaces $S$ of general type with ${p}_{g}=q=1$ having an involution $i$ such that $S/i$ has non-negative Kodaira dimension and that the bicanonical map of $S$ factors through the double cover induced by $i.$ It is shown that $S/i$ is regular and either: a) the Albanese fibration of $S$ is of genus 2 or b) $S$ has no genus 2 fibration and $S/i$ is birational to a $K3$ surface. For case a) a list of possibilities and examples are given. An example for case b) with ${K}^{2}=6$ is also constructed.

Classification:  14J29
@article{ASNSP_2007_5_6_1_81_0,
author = {Rito, Carlos},
title = {On surfaces with $p\_g = q = 1$ and non-ruled bicanonical involution},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {1},
year = {2007},
pages = {81-102},
zbl = {1180.14040},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_81_0}
}

Rito, Carlos. On surfaces with $p_g = q = 1$ and non-ruled bicanonical involution. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 81-102. http://www.numdam.org/item/ASNSP_2007_5_6_1_81_0/

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