We give a new construction of the irregular surfaces of general type with $p_g=5, \chi=2, K^ 2=8$, recently discovered by C. Schoen in \cite {Schoen}. Our approach proves that, if $S$ is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants $p_{g}=5, \chi=6, \, K^{2}=8$, a complete intersection of a quadric and a quartic hypersurface in $\PP^{4}$, with 40 even nodes.
Ciliberto, C., Lopes, M., Roulleau, X. (2015). On Schoen surfaces. COMMENTARII MATHEMATICI HELVETICI(90), 59-74 [10.4171/CMH/346].
On Schoen surfaces
CILIBERTO, CIRO;
2015-01-01
Abstract
We give a new construction of the irregular surfaces of general type with $p_g=5, \chi=2, K^ 2=8$, recently discovered by C. Schoen in \cite {Schoen}. Our approach proves that, if $S$ is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants $p_{g}=5, \chi=6, \, K^{2}=8$, a complete intersection of a quadric and a quartic hypersurface in $\PP^{4}$, with 40 even nodes.File in questo prodotto:
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