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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