On surfaces with p 𝑔 = q = 1 and non-ruled bicanonical involution

Carlos Rito

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 1, page 81-102
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Rito, Carlos. "On surfaces with p$_{\textit {g}}$ = q = 1 and non-ruled bicanonical involution." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.1 (2007): 81-102. <http://eudml.org/doc/272263>.

@article{Rito2007,
abstract = {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.},
author = {Rito, Carlos},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {involution; bicanonical map; irregular surface},
language = {eng},
number = {1},
pages = {81-102},
publisher = {Scuola Normale Superiore, Pisa},
title = {On surfaces with p$_\{\textit \{g\}\}$ = q = 1 and non-ruled bicanonical involution},
url = {http://eudml.org/doc/272263},
volume = {6},
year = {2007},
}

TY - JOUR
AU - Rito, Carlos
TI - On surfaces with p$_{\textit {g}}$ = q = 1 and non-ruled bicanonical involution
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 1
SP - 81
EP - 102
AB - 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.
LA - eng
KW - involution; bicanonical map; irregular surface
UR - http://eudml.org/doc/272263
ER -

References

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