JournalscmhVol. 90, No. 1pp. 59–74

On Schoen surfaces

  • Ciro Ciliberto

    Università di Roma, Italy
  • Margarida Mendes Lopes

    Instituto Superior Técnico, Lisboa, Portugal
  • Xavier Roulleau

    Université de Poitiers, Futuroscope Chasseneuil, France
On Schoen surfaces cover
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Abstract

We give a new construction of the irregular surfaces of general type with pg=5,χ=2,K2=8p_g=5, \chi=2, K^ 2=8,recently discovered by C. Schoen in [24]. Our approach proves that, if SS is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants pg=5,χ=6,K2=8p_{g}=5, \chi=6, \, K^{2}=8, a complete intersection of a quadric and a quartic hypersurface in P4\mathbb P^{4}, with 40 even nodes.

Cite this article

Ciro Ciliberto, Margarida Mendes Lopes, Xavier Roulleau, On Schoen surfaces. Comment. Math. Helv. 90 (2015), no. 1, pp. 59–74

DOI 10.4171/CMH/346