On surfaces with $p_g = q = 1$ and non-ruled bicanonical involution

Rito, Carlos

On surfaces with

p_{g} = q = 1

and non-ruled bicanonical involution

Rito, Carlos

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 1, pp. 81-102.

Résumé

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 $K 3$ surface. For case a) a list of possibilities and examples are given. An example for case b) with $K^{2} = 6$ is also constructed.

Zbl

Classification : 14J29

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     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},
     pages = {81--102},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {1},
     year = {2007},
     zbl = {1180.14040},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_81_0/}
}

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

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