New York Journal of Mathematics
Volume 27 (2021), 840-847


Chris Peters

On complex surfaces with definite intersection form

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Published: June 8, 2021.
Keywords: Compact complex surfaces, non-Kahler surfaces, intersection forms.
Subject: 14J80, 32J15.

A compact complex surface with positive definite intersection lattice is either the projective plane or a fake projective plane. If the intersection lattice is trivial or negative definite, the surface is either a secondary Kodaira surface, an elliptic surface with b1=1, or a class VII surface. If the lattice is non-trivial, it is odd and diagonalizable over the integers. There are no other cases of surfaces where the intersection lattice is definite.


The author expresses his thanks to the referees for making this note more readable.

Author information

Chris Peters:
Department of Mathematics and Computer Science
Eindhoven University of Technology
The Netherlands