Algebraic surfaces of general type with p_g=q=1 and genus 2 Albanese fibrations

• Autores: Songbo Ling
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 2, 2019, págs. 247-266
• Idioma: inglés
• DOI: 10.1007/s13348-018-0219-9
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• Resumen

  • In this paper, we study algebraic surfaces of general type with ??=?=1 and genus 2 Albanese fibrations. We first study the examples of surfaces with ??=?=1,?2=5 and genus 2 Albanese fibrations constructed by Catanese using singular bidouble covers of ℙ2 . We prove that these surfaces give an irreducible and connected component of 5,21,1 , the Gieseker moduli space of surfaces of general type with ??=?=1,?2=5 and genus 2 Albanese fibrations. Then by constructing surfaces with ??=?=1,?2=3 and a genus 2 Albanese fibration such that the number of the summands of the direct image of the bicanonical sheaf (under the Albanese map) is 2, we give a negative answer to a question of Pignatelli.